# -*- coding: utf-8 -*-
"""
This is a python implementation of the fast algorithm developed by
Vincent Mazet and Nicolas Chopin (see
http://miv.u-strasbg.fr/mazet/rtnorm/rtnorm-en.htm). The version this code
is based on is the Matlab implementation from 2012.

Created on Mon Aug 12 13:48:22 2013

@author: Christoph Lassner
"""
from scipy.special import erf
from numpy.random import uniform as rand, normal as randn, randint as randi
from numpy import sqrt, pi, exp, log, floor, array

def rtnorm(a, b, mu=0., sigma=1., size=1, probabilities=False):
    r"""
    Pseudorandom numbers from a truncated Gaussian distribution.
 
    X = rtnorm(a, b) returns a pseudorandom variable generated from a normal
    distribution with mean zero and variance one (i.e. standard normal
    distribution) truncated to the interval [a,b].
 
    X = rtnorm(a,b,mu,sigma) returns a pseudorandom variable generated from
    a normal distribution with mean MU and variance SIGMA truncated to the
    interval [a, b].
 
    The parameter size allows to specify a vector length and if probabilities
    is set to True, the function also returns the vector of probabilities of X.

    This implements an extension of Chopin's algorithm detailed in
    N. Chopin, "Fast simulation of truncated Gaussian distributions", Stat
    Comput (2011) 21:275-288
 
    Copyright (C) 2012 Vincent Mazet (LSIIT, CNRS/Université de Strasbourg),
    Version 2012-07-04, vincent.mazet@unistra.fr

    08/12/2013:
     - created python version.
    18/06/2012:
     - first launch of rtnorm.m
    05/07/2012:
     - fix bug concerning the computing of the pdf when (mu,sigma) is
       different from (0,1). 
     - fix bug about some indexes out of bounds when computing yl for some
       values of the input arguments.
    04/09/2012:
     - change condition in line 2628 to fix a bug.
 
    Licence: GNU General Public License Version 2
    This program is free software; you can redistribute it and/or modify it
    under the terms of the GNU General Public License as published by the
    Free Software Foundation; either version 2 of the License, or (at your
    option) any later version. This program is distributed in the hope that
    it will be useful, but WITHOUT ANY WARRANTY; without even the implied
    warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details. You should have received a
    copy of the GNU General Public License along with this program; if not,
    see http://www.gnu.org/licenses/old-licenses/gpl-2.0.txt.
    
    """
    # Ensure these are floats for proper division values later on.
    mu = float(mu)
    sigma = float(sigma)
    a = float(a)
    b = float(b)

    # Scaling
    if not mu == 0. or not sigma == 1.:
        a = (a-mu) / sigma
        b = (b-mu) / sigma

    # Generate the random variables
    r = array([rtstdnorm(a, b) for x in range(size)])

    # Scaling
    if not mu == 0. or not sigma == 1.:
        r = r * sigma + mu

    # Compute the probabilities
    if probabilities:
        Z = sqrt(pi/2)*sigma * (erf(b/sqrt(2))-erf(a/sqrt(2)))
        Z = max(Z, 1e-15)      # Avoid NaN
        p = exp(-(r-mu)**2/2/sigma**2) / Z
        return r, p
    else:
        return r


def rtstdnorm(a, b):
    r"""
    RTNORM    Pseudorandom numbers from a truncated (normalized) Gaussian
    distribution (i.e. rtnorm(a,b,0,1)).
    """
    # Left and right limits
    xmin = -2.00443204036
    xmax = 3.48672170399

    # Check if a < b
    if a >= b:
        raise Exception('For a truncated ndst in [a,b] b must be greater than a.')    
    # Check if |a| < |b|
    elif abs(a) > abs(b):
        r = -rtstdnorm(-b, -a)
    # If a in the right tail (a > xmax), use rejection algorithm with
    # a truncated exponential proposal
    elif a > xmax:
        stop = False
        twoasq = 2*a**2
        expab = exp(-a*(b-a)) - 1
        while not stop:
            # The rand-function in Matlab that was used here returns values
            # uniformly distributed in (0, 1). The numpy version includes
            # the left border of the interval, so the numbers are drawn from
            # [0, 1). Hence use a low lower border.
            z = log(1 + rand(low=1E-15)*expab)
            e = -log(rand(low=1E-15))
            stop = (twoasq*e > z ** 2)
        r = a - z/a
    # If a in the left tail (a < xmin), use rejection algorithm with
    # a Gaussian proposal
    elif a < xmin:
        stop = False
        while not stop:
            r = randn()
            stop = (r>=a) and (r<=b)
    # In other cases (xmin < a < xmax), use Chopin's algorithm
    else:    
        # Design variables
        kmin = 5                        # if kb-ka < kmin then use a rejection algorithm
        INVH = 1631.73284006            # 1/h, h being the minimal interval range
        I0 = 3271                       # = - floor(x(1)/h)
        ALPHA = 1.837877066409345       # = log(2*pi)
        N = 4000                        # Index of the right tail
        yl0 = 0.053513975472            # y_l of the leftmost rectangle
        ylN = 0.000914116389555         # y_l of the rightmost rectangle

        # Compute ka and kb
        i = int(I0 + floor(a*INVH))
        ka = ncell[i]                   # not: +1 due to index offset in Matlab ;-)
        kb = 0
        if b >= xmax:
            kb = N
        else:
            i = int(I0 + floor(b*INVH))
            kb = ncell[i]               # not: +1 due to index offset in Matlab
    
        # If |b-a| is small, use rejection algorithm with a truncated exponential proposal
        if abs(kb-ka) < kmin:        
            stop = False
            twoasq = 2 * a**2
            expab = exp(-a*(b-a)) - 1
            while not stop:
                z = log( 1 + rand()*expab )
                e = -log(rand())
                stop = (twoasq*e > z**2)
            r = a - z/a
            return r
        while True:
            # Sample integer between ka and kb
            # Note that while matlab randi has including border, for numpy the high
            # border is exclusive. Hence add one.
            k = randi(low=ka, high=(kb+1))      # not: +1 due to index offset in Matlab        
            if k == N:
                # Right tail
                lbound = x[-1]
                z = -log(rand())
                e = -log(rand())
                z = z / lbound
                if (z**2 <= 2*e) and (z < b-lbound):
                    # Accept this proposition, otherwise reject
                    r = lbound + z
                    return r
            elif (k<=ka+2) or (k>=kb and b<xmax):
                # Two leftmost and rightmost regions
                sim = x[k] + (x[k+1]-x[k]) * rand()
                if (sim >= a) and (sim <= b):
                    # Accept this proposition, otherwise reject
                    simy = yu[k]*rand()
    
                    # Compute y_l from y_k
                    if k == 0:
                       ylk = yl0
                    elif k == N:
                       ylk = ylN
                    elif k <= 1954:
                        ylk = yu[k-1]
                    else:
                        ylk = yu[k+1]
                    
                    if (simy<ylk) or (sim**2 + 2*log(simy) + ALPHA < 0):
                        r = sim
                        return r
            else:
                # All the other boxes
                u = rand()
                simy = yu[k] * u
                d = x[k+1] - x[k]
                
                # Compute y_l from y_k
                if k == 1:
                    ylk = yl0
                elif k == N:
                    ylk = ylN
                elif k <= 1954:
                    ylk = yu[k-1]
                else:
                    ylk = yu[k+1]
                    
                if simy < ylk:  # That's what happens most of the time 
                    r = x[k] + u*d*yu[k]/ylk
                    return r
                sim = x[k] + d * rand()
                # Otherwise, check you're below the pdf curve
                if sim**2 + 2*log(simy) + ALPHA < 0:
                    r = sim
                    return r
    return r


        # Tables
x = array([
    -2.00443204036, -1.99990455547, -1.99541747213, -1.99096998962, \
    -1.98656133124, -1.98219074335, -1.97785749442, -1.97356087419, \
    -1.96930019287, -1.96507478031, -1.96088398528, -1.95672717477, \
    -1.95260373328, -1.9485130622, -1.94445457918, -1.94042771755, \
    -1.93643192574, -1.93246666677, -1.92853141772, -1.92462566922, \
    -1.92074892503, -1.91690070156, -1.91308052741, -1.90928794302, \
    -1.90552250025, -1.90178376197, -1.89807130174, -1.89438470345, \
    -1.89072356098, -1.88708747787, -1.88347606705, -1.8798889505, \
    -1.87632575899, -1.87278613181, -1.86926971649, -1.86577616858, \
    -1.86230515137, -1.85885633567, -1.8554293996, -1.85202402837, \
    -1.84863991405, -1.84527675539, -1.84193425762, -1.83861213227, \
    -1.83531009698, -1.83202787533, -1.82876519668, -1.825521796, \
    -1.82229741372, -1.81909179558, -1.81590469249, -1.81273586036, \
    -1.80958506, -1.80645205698, -1.8033366215, -1.80023852827, \
    -1.79715755637, -1.79409348917, -1.79104611422, -1.78801522309, \
    -1.78500061134, -1.78200207837, -1.77901942732, -1.77605246501, \
    -1.77310100183, -1.77016485166, -1.76724383175, -1.7643377627, \
    -1.7614464683, -1.75856977555, -1.75570751448, -1.75285951816, \
    -1.75002562257, -1.74720566658, -1.74439949184, -1.74160694276, \
    -1.73882786639, -1.7360621124, -1.73330953303, -1.73056998298, \
    -1.72784331941, -1.72512940185, -1.72242809217, -1.71973925449, \
    -1.71706275519, -1.7143984628, -1.71174624799, -1.70910598353, \
    -1.70647754419, -1.70386080677, -1.70125565, -1.69866195455, \
    -1.69607960292, -1.69350847947, -1.69094847035, -1.68839946345, \
    -1.6858613484, -1.68333401649, -1.68081736069, -1.67831127556, \
    -1.67581565725, -1.67333040348, -1.67085541345, -1.6683905879, \
    -1.665935829, -1.66349104035, -1.66105612696, -1.65863099522, \
    -1.65621555288, -1.65380970898, -1.65141337389, -1.64902645924, \
    -1.64664887792, -1.64428054402, -1.64192137286, -1.63957128092, \
    -1.63723018585, -1.63489800643, -1.63257466256, -1.63026007522, \
    -1.62795416649, -1.62565685948, -1.62336807836, -1.62108774828, \
    -1.61881579544, -1.61655214696, -1.61429673098, -1.61204947656, \
    -1.60981031368, -1.60757917325, -1.60535598708, -1.60314068784, \
    -1.60093320909, -1.59873348523, -1.59654145149, -1.59435704393, \
    -1.59218019943, -1.59001085565, -1.58784895103, -1.58569442477, \
    -1.58354721686, -1.581407268, -1.57927451964, -1.57714891392, \
    -1.57503039371, -1.57291890258, -1.57081438477, -1.56871678519, \
    -1.56662604942, -1.56454212368, -1.56246495486, -1.56039449044, \
    -1.55833067854, -1.55627346789, -1.55422280782, -1.55217864825, \
    -1.55014093969, -1.5481096332, -1.54608468043, -1.54406603357, \
    -1.54205364536, -1.54004746908, -1.53804745854, -1.53605356807, \
    -1.53406575252, -1.53208396723, -1.53010816806, -1.52813831134, \
    -1.52617435391, -1.52421625305, -1.52226396655, -1.52031745264, \
    -1.51837667, -1.51644157777, -1.51451213554, -1.51258830332, \
    -1.51067004156, -1.50875731112, -1.5068500733, -1.50494828979, \
    -1.50305192269, -1.50116093452, -1.49927528818, -1.49739494693, \
    -1.49551987447, -1.49365003484, -1.49178539245, -1.48992591209, \
    -1.48807155892, -1.48622229844, -1.48437809651, -1.48253891934, \
    -1.48070473348, -1.47887550581, -1.47705120356, -1.47523179427, \
    -1.47341724582, -1.47160752641, -1.46980260454, -1.46800244903, \
    -1.46620702902, -1.46441631394, -1.46263027351, -1.46084887778, \
    -1.45907209704, -1.45729990192, -1.4555322633, -1.45376915236, \
    -1.45201054053, -1.45025639954, -1.44850670139, -1.44676141832, \
    -1.44502052286, -1.44328398779, -1.44155178613, -1.43982389118, \
    -1.43810027647, -1.43638091579, -1.43466578316, -1.43295485285, \
    -1.43124809936, -1.42954549744, -1.42784702206, -1.4261526484, \
    -1.42446235191, -1.42277610822, -1.42109389321, -1.41941568296, \
    -1.41774145377, -1.41607118216, -1.41440484485, -1.41274241877, \
    -1.41108388106, -1.40942920906, -1.40777838029, -1.40613137251, \
    -1.40448816364, -1.40284873181, -1.40121305532, -1.39958111269, \
    -1.3979528826, -1.39632834393, -1.39470747574, -1.39309025725, \
    -1.39147666789, -1.38986668723, -1.38826029505, -1.38665747129, \
    -1.38505819603, -1.38346244956, -1.38187021232, -1.3802814649, \
    -1.37869618807, -1.37711436276, -1.37553597004, -1.37396099116, \
    -1.37238940752, -1.37082120066, -1.36925635228, -1.36769484423, \
    -1.36613665852, -1.36458177727, -1.3630301828, -1.36148185752, \
    -1.35993678401, -1.35839494499, -1.35685632332, -1.35532090198, \
    -1.3537886641, -1.35225959295, -1.35073367192, -1.34921088453, \
    -1.34769121444, -1.34617464545, -1.34466116145, -1.34315074649, \
    -1.34164338473, -1.34013906045, -1.33863775808, -1.33713946213, \
    -1.33564415726, -1.33415182822, -1.33266245992, -1.33117603734, \
    -1.3296925456, -1.32821196994, -1.32673429568, -1.32525950829, \
    -1.32378759331, -1.32231853644, -1.32085232344, -1.31938894019, \
    -1.3179283727, -1.31647060705, -1.31501562944, -1.31356342618, \
    -1.31211398366, -1.31066728839, -1.30922332698, -1.30778208612, \
    -1.30634355261, -1.30490771336, -1.30347455533, -1.30204406564, \
    -1.30061623144, -1.29919104001, -1.29776847873, -1.29634853503, \
    -1.29493119647, -1.29351645068, -1.29210428538, -1.29069468838, \
    -1.28928764758, -1.28788315096, -1.28648118658, -1.2850817426, \
    -1.28368480725, -1.28229036885, -1.2808984158, -1.27950893658, \
    -1.27812191975, -1.27673735394, -1.27535522788, -1.27397553036, \
    -1.27259825027, -1.27122337654, -1.2698508982, -1.26848080436, \
    -1.26711308419, -1.26574772695, -1.26438472195, -1.26302405859, \
    -1.26166572634, -1.26030971474, -1.25895601339, -1.25760461198, \
    -1.25625550025, -1.25490866802, -1.25356410517, -1.25222180165, \
    -1.25088174749, -1.24954393277, -1.24820834764, -1.24687498231, \
    -1.24554382707, -1.24421487225, -1.24288810826, -1.24156352558, \
    -1.24024111474, -1.23892086632, -1.23760277098, -1.23628681945, \
    -1.23497300248, -1.23366131092, -1.23235173565, -1.23104426764, \
    -1.22973889789, -1.22843561746, -1.22713441748, -1.22583528914, \
    -1.22453822366, -1.22324321234, -1.22195024653, -1.22065931762, \
    -1.21937041707, -1.2180835364, -1.21679866716, -1.21551580096, \
    -1.21423492948, -1.21295604444, -1.21167913759, -1.21040420078, \
    -1.20913122586, -1.20786020475, -1.20659112944, -1.20532399194, \
    -1.20405878432, -1.2027954987, -1.20153412724, -1.20027466216, \
    -1.19901709572, -1.19776142023, -1.19650762804, -1.19525571156, \
    -1.19400566322, -1.19275747553, -1.19151114101, -1.19026665225, \
    -1.18902400188, -1.18778318256, -1.18654418701, -1.18530700798, \
    -1.18407163828, -1.18283807074, -1.18160629825, -1.18037631374, \
    -1.17914811017, -1.17792168055, -1.17669701793, -1.1754741154, \
    -1.17425296609, -1.17303356317, -1.17181589985, -1.17059996938, \
    -1.16938576505, -1.16817328018, -1.16696250814, -1.16575344233, \
    -1.1645460762, -1.16334040321, -1.16213641689, -1.16093411079, \
    -1.1597334785, -1.15853451364, -1.15733720988, -1.1561415609, \
    -1.15494756045, -1.1537552023, -1.15256448023, -1.1513753881, \
    -1.15018791978, -1.14900206916, -1.1478178302, -1.14663519686, \
    -1.14545416315, -1.14427472312, -1.14309687083, -1.14192060039, \
    -1.14074590595, -1.13957278166, -1.13840122174, -1.13723122041, \
    -1.13606277195, -1.13489587064, -1.13373051083, -1.13256668686, \
    -1.13140439313, -1.13024362405, -1.12908437408, -1.12792663769, \
    -1.1267704094, -1.12561568374, -1.12446245528, -1.12331071862, \
    -1.12216046839, -1.12101169923, -1.11986440583, -1.1187185829, \
    -1.11757422519, -1.11643132745, -1.11528988448, -1.11414989111, \
    -1.11301134218, -1.11187423257, -1.11073855719, -1.10960431095, \
    -1.10847148882, -1.10734008578, -1.10621009684, -1.10508151703, \
    -1.10395434141, -1.10282856507, -1.10170418311, -1.10058119068, \
    -1.09945958293, -1.09833935506, -1.09722050226, -1.09610301977, \
    -1.09498690286, -1.09387214681, -1.09275874692, -1.09164669853, \
    -1.09053599698, -1.08942663766, -1.08831861598, -1.08721192734, \
    -1.08610656721, -1.08500253104, -1.08389981434, -1.08279841262, \
    -1.08169832142, -1.0805995363, -1.07950205283, -1.07840586663, \
    -1.07731097332, -1.07621736855, -1.07512504799, -1.07403400732, \
    -1.07294424226, -1.07185574854, -1.07076852192, -1.06968255816, \
    -1.06859785307, -1.06751440246, -1.06643220217, -1.06535124805, \
    -1.06427153597, -1.06319306184, -1.06211582157, -1.06103981109, \
    -1.05996502636, -1.05889146336, -1.05781911808, -1.05674798653, \
    -1.05567806475, -1.05460934878, -1.0535418347, -1.0524755186, \
    -1.05141039657, -1.05034646476, -1.04928371929, -1.04822215635, \
    -1.04716177209, -1.04610256273, -1.04504452448, -1.04398765357, \
    -1.04293194626, -1.04187739881, -1.04082400752, -1.03977176868, \
    -1.03872067861, -1.03767073366, -1.03662193018, -1.03557426455, \
    -1.03452773314, -1.03348233237, -1.03243805866, -1.03139490845, \
    -1.03035287819, -1.02931196435, -1.02827216342, -1.02723347191, \
    -1.02619588633, -1.02515940322, -1.02412401912, -1.02308973062, \
    -1.02205653428, -1.02102442671, -1.01999340452, -1.01896346433, \
    -1.01793460279, -1.01690681657, -1.01588010232, -1.01485445675, \
    -1.01382987655, -1.01280635844, -1.01178389916, -1.01076249545, \
    -1.00974214407, -1.0087228418, -1.00770458543, -1.00668737176, \
    -1.00567119762, -1.00465605983, -1.00364195524, -1.00262888071, \
    -1.00161683312, -1.00060580935, -0.999595806306, -0.9985868209, \
    -0.997578850062, -0.996571890733, -0.995565939868, -0.994560994436, \
    -0.993557051418, -0.992554107808, -0.991552160613, -0.990551206854, \
    -0.989551243564, -0.988552267788, -0.987554276585, -0.986557267027, \
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    0.0393906098197, 0.0388672464844, 0.0383424230521, 0.0378161210995, \
    0.037288321689, 0.0367590053466, 0.0362281520387, 0.0356957411476, \
    0.0351617514458, 0.034626161068, 0.0340889474822, 0.0335500874589, \
    0.033009557038, 0.032467331494, 0.0319233852988, 0.0313776920821, \
    0.0308302245895, 0.0302809546372, 0.0297298530646, 0.0291768896823, \
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    0.02638300979, 0.0258181765805, 0.0252512363179, 0.0246821482486, \
    0.0241108699283, 0.0235373571186, 0.0229615636755, 0.0223834414285, \
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    0.0194560530967, 0.0188628152806, 0.0182668424588, 0.0176680646372, \
    0.0170664082066, 0.016461795704, 0.0158541455627, 0.015243371858, \
    0.0146293840521, 0.0140120867521, 0.0133913794939, 0.0127671565806, \
    0.0121393070128, 0.0115077145716, 0.0108722581496, 0.0102328124764, \
    0.00958924947315, 0.00894144061242, 0.00828926090091, 0.00763259551896, \
    0.00697135089651, 0.00630547338383, 0.00563498133279, 0.00496002177703, \
    0.00428097439553, 0.00359865177269, 0.00291471045349, 0.00223256762114, \
    0.00155968193081 ])

ncell = array([
    0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, \
    2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, \
    5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, \
    8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, \
    11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, \
    14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, \
    17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 20, \
    20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, \
    23, 23, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, \
    27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 29, 29, 29, 29, 29, 29, 30, 30, \
    30, 30, 30, 30, 31, 31, 31, 31, 31, 31, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, \
    33, 34, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 37, 37, \
    37, 37, 37, 37, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 40, 40, 40, 40, 40, \
    40, 41, 41, 41, 41, 41, 42, 42, 42, 42, 42, 43, 43, 43, 43, 43, 43, 44, 44, 44, \
    44, 44, 45, 45, 45, 45, 45, 46, 46, 46, 46, 46, 46, 47, 47, 47, 47, 47, 48, 48, \
    48, 48, 48, 49, 49, 49, 49, 49, 50, 50, 50, 50, 50, 50, 51, 51, 51, 51, 51, 52, \
    52, 52, 52, 52, 53, 53, 53, 53, 53, 54, 54, 54, 54, 54, 55, 55, 55, 55, 55, 56, \
    56, 56, 56, 56, 57, 57, 57, 57, 57, 58, 58, 58, 58, 58, 59, 59, 59, 59, 59, 60, \
    60, 60, 60, 60, 61, 61, 61, 61, 61, 62, 62, 62, 62, 63, 63, 63, 63, 63, 64, 64, \
    64, 64, 64, 65, 65, 65, 65, 65, 66, 66, 66, 66, 66, 67, 67, 67, 67, 68, 68, 68, \
    68, 68, 69, 69, 69, 69, 69, 70, 70, 70, 70, 71, 71, 71, 71, 71, 72, 72, 72, 72, \
    72, 73, 73, 73, 73, 74, 74, 74, 74, 74, 75, 75, 75, 75, 76, 76, 76, 76, 76, 77, \
    77, 77, 77, 78, 78, 78, 78, 78, 79, 79, 79, 79, 80, 80, 80, 80, 80, 81, 81, 81, \
    81, 82, 82, 82, 82, 83, 83, 83, 83, 83, 84, 84, 84, 84, 85, 85, 85, 85, 86, 86, \
    86, 86, 86, 87, 87, 87, 87, 88, 88, 88, 88, 89, 89, 89, 89, 89, 90, 90, 90, 90, \
    91, 91, 91, 91, 92, 92, 92, 92, 93, 93, 93, 93, 94, 94, 94, 94, 95, 95, 95, 95, \
    95, 96, 96, 96, 96, 97, 97, 97, 97, 98, 98, 98, 98, 99, 99, 99, 99, 100, 100, 100, \
    100, 101, 101, 101, 101, 102, 102, 102, 102, 103, 103, 103, 103, 104, 104, 104, 104, 105, 105, 105, \
    105, 106, 106, 106, 106, 107, 107, 107, 107, 108, 108, 108, 108, 109, 109, 109, 109, 110, 110, 110, \
    110, 111, 111, 111, 111, 112, 112, 112, 113, 113, 113, 113, 114, 114, 114, 114, 115, 115, 115, 115, \
    116, 116, 116, 116, 117, 117, 117, 117, 118, 118, 118, 119, 119, 119, 119, 120, 120, 120, 120, 121, \
    121, 121, 121, 122, 122, 122, 123, 123, 123, 123, 124, 124, 124, 124, 125, 125, 125, 126, 126, 126, \
    126, 127, 127, 127, 127, 128, 128, 128, 129, 129, 129, 129, 130, 130, 130, 130, 131, 131, 131, 132, \
    132, 132, 132, 133, 133, 133, 134, 134, 134, 134, 135, 135, 135, 136, 136, 136, 136, 137, 137, 137, \
    137, 138, 138, 138, 139, 139, 139, 139, 140, 140, 140, 141, 141, 141, 141, 142, 142, 142, 143, 143, \
    143, 144, 144, 144, 144, 145, 145, 145, 146, 146, 146, 146, 147, 147, 147, 148, 148, 148, 148, 149, \
    149, 149, 150, 150, 150, 151, 151, 151, 151, 152, 152, 152, 153, 153, 153, 154, 154, 154, 154, 155, \
    155, 155, 156, 156, 156, 157, 157, 157, 157, 158, 158, 158, 159, 159, 159, 160, 160, 160, 160, 161, \
    161, 161, 162, 162, 162, 163, 163, 163, 164, 164, 164, 164, 165, 165, 165, 166, 166, 166, 167, 167, \
    167, 168, 168, 168, 169, 169, 169, 169, 170, 170, 170, 171, 171, 171, 172, 172, 172, 173, 173, 173, \
    174, 174, 174, 175, 175, 175, 176, 176, 176, 176, 177, 177, 177, 178, 178, 178, 179, 179, 179, 180, \
    180, 180, 181, 181, 181, 182, 182, 182, 183, 183, 183, 184, 184, 184, 185, 185, 185, 186, 186, 186, \
    187, 187, 187, 188, 188, 188, 189, 189, 189, 190, 190, 190, 191, 191, 191, 192, 192, 192, 193, 193, \
    193, 194, 194, 194, 195, 195, 195, 196, 196, 196, 197, 197, 197, 198, 198, 198, 199, 199, 199, 200, \
    200, 200, 201, 201, 201, 202, 202, 202, 203, 203, 203, 204, 204, 204, 205, 205, 206, 206, 206, 207, \
    207, 207, 208, 208, 208, 209, 209, 209, 210, 210, 210, 211, 211, 211, 212, 212, 213, 213, 213, 214, \
    214, 214, 215, 215, 215, 216, 216, 216, 217, 217, 217, 218, 218, 219, 219, 219, 220, 220, 220, 221, \
    221, 221, 222, 222, 223, 223, 223, 224, 224, 224, 225, 225, 225, 226, 226, 227, 227, 227, 228, 228, \
    228, 229, 229, 229, 230, 230, 231, 231, 231, 232, 232, 232, 233, 233, 234, 234, 234, 235, 235, 235, \
    236, 236, 237, 237, 237, 238, 238, 238, 239, 239, 240, 240, 240, 241, 241, 241, 242, 242, 243, 243, \
    243, 244, 244, 244, 245, 245, 246, 246, 246, 247, 247, 248, 248, 248, 249, 249, 249, 250, 250, 251, \
    251, 251, 252, 252, 253, 253, 253, 254, 254, 254, 255, 255, 256, 256, 256, 257, 257, 258, 258, 258, \
    259, 259, 260, 260, 260, 261, 261, 262, 262, 262, 263, 263, 264, 264, 264, 265, 265, 266, 266, 266, \
    267, 267, 268, 268, 268, 269, 269, 270, 270, 270, 271, 271, 272, 272, 272, 273, 273, 274, 274, 274, \
    275, 275, 276, 276, 276, 277, 277, 278, 278, 278, 279, 279, 280, 280, 280, 281, 281, 282, 282, 283, \
    283, 283, 284, 284, 285, 285, 285, 286, 286, 287, 287, 288, 288, 288, 289, 289, 290, 290, 290, 291, \
    291, 292, 292, 293, 293, 293, 294, 294, 295, 295, 296, 296, 296, 297, 297, 298, 298, 298, 299, 299, \
    300, 300, 301, 301, 301, 302, 302, 303, 303, 304, 304, 304, 305, 305, 306, 306, 307, 307, 307, 308, \
    308, 309, 309, 310, 310, 311, 311, 311, 312, 312, 313, 313, 314, 314, 314, 315, 315, 316, 316, 317, \
    317, 318, 318, 318, 319, 319, 320, 320, 321, 321, 322, 322, 322, 323, 323, 324, 324, 325, 325, 326, \
    326, 326, 327, 327, 328, 328, 329, 329, 330, 330, 330, 331, 331, 332, 332, 333, 333, 334, 334, 335, \
    335, 335, 336, 336, 337, 337, 338, 338, 339, 339, 340, 340, 340, 341, 341, 342, 342, 343, 343, 344, \
    344, 345, 345, 346, 346, 346, 347, 347, 348, 348, 349, 349, 350, 350, 351, 351, 352, 352, 353, 353, \
    353, 354, 354, 355, 355, 356, 356, 357, 357, 358, 358, 359, 359, 360, 360, 361, 361, 361, 362, 362, \
    363, 363, 364, 364, 365, 365, 366, 366, 367, 367, 368, 368, 369, 369, 370, 370, 371, 371, 371, 372, \
    372, 373, 373, 374, 374, 375, 375, 376, 376, 377, 377, 378, 378, 379, 379, 380, 380, 381, 381, 382, \
    382, 383, 383, 384, 384, 385, 385, 386, 386, 387, 387, 388, 388, 389, 389, 390, 390, 391, 391, 392, \
    392, 393, 393, 394, 394, 395, 395, 396, 396, 397, 397, 398, 398, 399, 399, 400, 400, 401, 401, 402, \
    402, 403, 403, 404, 404, 405, 405, 406, 406, 407, 407, 408, 408, 409, 409, 410, 410, 411, 411, 412, \
    412, 413, 413, 414, 414, 415, 415, 416, 416, 417, 417, 418, 418, 419, 419, 420, 420, 421, 421, 422, \
    423, 423, 424, 424, 425, 425, 426, 426, 427, 427, 428, 428, 429, 429, 430, 430, 431, 431, 432, 432, \
    433, 433, 434, 435, 435, 436, 436, 437, 437, 438, 438, 439, 439, 440, 440, 441, 441, 442, 442, 443, \
    444, 444, 445, 445, 446, 446, 447, 447, 448, 448, 449, 449, 450, 450, 451, 452, 452, 453, 453, 454, \
    454, 455, 455, 456, 456, 457, 458, 458, 459, 459, 460, 460, 461, 461, 462, 462, 463, 464, 464, 465, \
    465, 466, 466, 467, 467, 468, 468, 469, 470, 470, 471, 471, 472, 472, 473, 473, 474, 475, 475, 476, \
    476, 477, 477, 478, 478, 479, 480, 480, 481, 481, 482, 482, 483, 483, 484, 485, 485, 486, 486, 487, \
    487, 488, 488, 489, 490, 490, 491, 491, 492, 492, 493, 494, 494, 495, 495, 496, 496, 497, 498, 498, \
    499, 499, 500, 500, 501, 502, 502, 503, 503, 504, 504, 505, 506, 506, 507, 507, 508, 508, 509, 510, \
    510, 511, 511, 512, 512, 513, 514, 514, 515, 515, 516, 517, 517, 518, 518, 519, 519, 520, 521, 521, \
    522, 522, 523, 524, 524, 525, 525, 526, 526, 527, 528, 528, 529, 529, 530, 531, 531, 532, 532, 533, \
    534, 534, 535, 535, 536, 537, 537, 538, 538, 539, 539, 540, 541, 541, 542, 542, 543, 544, 544, 545, \
    545, 546, 547, 547, 548, 548, 549, 550, 550, 551, 551, 552, 553, 553, 554, 555, 555, 556, 556, 557, \
    558, 558, 559, 559, 560, 561, 561, 562, 562, 563, 564, 564, 565, 565, 566, 567, 567, 568, 569, 569, \
    570, 570, 571, 572, 572, 573, 573, 574, 575, 575, 576, 577, 577, 578, 578, 579, 580, 580, 581, 582, \
    582, 583, 583, 584, 585, 585, 586, 586, 587, 588, 588, 589, 590, 590, 591, 591, 592, 593, 593, 594, \
    595, 595, 596, 597, 597, 598, 598, 599, 600, 600, 601, 602, 602, 603, 603, 604, 605, 605, 606, 607, \
    607, 608, 609, 609, 610, 610, 611, 612, 612, 613, 614, 614, 615, 616, 616, 617, 618, 618, 619, 619, \
    620, 621, 621, 622, 623, 623, 624, 625, 625, 626, 627, 627, 628, 629, 629, 630, 630, 631, 632, 632, \
    633, 634, 634, 635, 636, 636, 637, 638, 638, 639, 640, 640, 641, 642, 642, 643, 644, 644, 645, 646, \
    646, 647, 647, 648, 649, 649, 650, 651, 651, 652, 653, 653, 654, 655, 655, 656, 657, 657, 658, 659, \
    659, 660, 661, 661, 662, 663, 663, 664, 665, 665, 666, 667, 667, 668, 669, 669, 670, 671, 671, 672, \
    673, 674, 674, 675, 676, 676, 677, 678, 678, 679, 680, 680, 681, 682, 682, 683, 684, 684, 685, 686, \
    686, 687, 688, 688, 689, 690, 690, 691, 692, 693, 693, 694, 695, 695, 696, 697, 697, 698, 699, 699, \
    700, 701, 701, 702, 703, 704, 704, 705, 706, 706, 707, 708, 708, 709, 710, 710, 711, 712, 713, 713, \
    714, 715, 715, 716, 717, 717, 718, 719, 719, 720, 721, 722, 722, 723, 724, 724, 725, 726, 726, 727, \
    728, 729, 729, 730, 731, 731, 732, 733, 734, 734, 735, 736, 736, 737, 738, 738, 739, 740, 741, 741, \
    742, 743, 743, 744, 745, 746, 746, 747, 748, 748, 749, 750, 751, 751, 752, 753, 753, 754, 755, 756, \
    756, 757, 758, 758, 759, 760, 761, 761, 762, 763, 763, 764, 765, 766, 766, 767, 768, 769, 769, 770, \
    771, 771, 772, 773, 774, 774, 775, 776, 777, 777, 778, 779, 779, 780, 781, 782, 782, 783, 784, 785, \
    785, 786, 787, 787, 788, 789, 790, 790, 791, 792, 793, 793, 794, 795, 796, 796, 797, 798, 798, 799, \
    800, 801, 801, 802, 803, 804, 804, 805, 806, 807, 807, 808, 809, 810, 810, 811, 812, 813, 813, 814, \
    815, 816, 816, 817, 818, 819, 819, 820, 821, 822, 822, 823, 824, 825, 825, 826, 827, 828, 828, 829, \
    830, 831, 831, 832, 833, 834, 834, 835, 836, 837, 837, 838, 839, 840, 840, 841, 842, 843, 843, 844, \
    845, 846, 846, 847, 848, 849, 849, 850, 851, 852, 853, 853, 854, 855, 856, 856, 857, 858, 859, 859, \
    860, 861, 862, 862, 863, 864, 865, 866, 866, 867, 868, 869, 869, 870, 871, 872, 872, 873, 874, 875, \
    876, 876, 877, 878, 879, 879, 880, 881, 882, 883, 883, 884, 885, 886, 886, 887, 888, 889, 890, 890, \
    891, 892, 893, 893, 894, 895, 896, 897, 897, 898, 899, 900, 900, 901, 902, 903, 904, 904, 905, 906, \
    907, 908, 908, 909, 910, 911, 911, 912, 913, 914, 915, 915, 916, 917, 918, 919, 919, 920, 921, 922, \
    923, 923, 924, 925, 926, 927, 927, 928, 929, 930, 931, 931, 932, 933, 934, 935, 935, 936, 937, 938, \
    939, 939, 940, 941, 942, 943, 943, 944, 945, 946, 947, 947, 948, 949, 950, 951, 951, 952, 953, 954, \
    955, 955, 956, 957, 958, 959, 959, 960, 961, 962, 963, 963, 964, 965, 966, 967, 968, 968, 969, 970, \
    971, 972, 972, 973, 974, 975, 976, 976, 977, 978, 979, 980, 981, 981, 982, 983, 984, 985, 985, 986, \
    987, 988, 989, 990, 990, 991, 992, 993, 994, 994, 995, 996, 997, 998, 999, 999, 1000, 1001, 1002, 1003, \
    1004, 1004, 1005, 1006, 1007, 1008, 1008, 1009, 1010, 1011, 1012, 1013, 1013, 1014, 1015, 1016, 1017, 1018, 1018, 1019, \
    1020, 1021, 1022, 1023, 1023, 1024, 1025, 1026, 1027, 1028, 1028, 1029, 1030, 1031, 1032, 1033, 1033, 1034, 1035, 1036, \
    1037, 1038, 1038, 1039, 1040, 1041, 1042, 1043, 1044, 1044, 1045, 1046, 1047, 1048, 1049, 1049, 1050, 1051, 1052, 1053, \
    1054, 1054, 1055, 1056, 1057, 1058, 1059, 1060, 1060, 1061, 1062, 1063, 1064, 1065, 1065, 1066, 1067, 1068, 1069, 1070, \
    1071, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1077, 1078, 1079, 1080, 1081, 1082, 1082, 1083, 1084, 1085, 1086, 1087, \
    1088, 1088, 1089, 1090, 1091, 1092, 1093, 1094, 1094, 1095, 1096, 1097, 1098, 1099, 1100, 1100, 1101, 1102, 1103, 1104, \
    1105, 1106, 1107, 1107, 1108, 1109, 1110, 1111, 1112, 1113, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1119, 1120, 1121, \
    1122, 1123, 1124, 1125, 1126, 1126, 1127, 1128, 1129, 1130, 1131, 1132, 1133, 1133, 1134, 1135, 1136, 1137, 1138, 1139, \
    1139, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1146, 1147, 1148, 1149, 1150, 1151, 1152, 1153, 1153, 1154, 1155, 1156, \
    1157, 1158, 1159, 1160, 1161, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1168, 1169, 1170, 1171, 1172, 1173, 1174, \
    1175, 1176, 1176, 1177, 1178, 1179, 1180, 1181, 1182, 1183, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 1190, 1191, 1191, \
    1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 1199, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1208, 1209, \
    1210, 1211, 1212, 1213, 1214, 1215, 1216, 1216, 1217, 1218, 1219, 1220, 1221, 1222, 1223, 1224, 1225, 1225, 1226, 1227, \
    1228, 1229, 1230, 1231, 1232, 1233, 1234, 1234, 1235, 1236, 1237, 1238, 1239, 1240, 1241, 1242, 1243, 1243, 1244, 1245, \
    1246, 1247, 1248, 1249, 1250, 1251, 1252, 1253, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 1260, 1261, 1262, 1263, 1263, \
    1264, 1265, 1266, 1267, 1268, 1269, 1270, 1271, 1272, 1273, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 1280, 1281, 1282, \
    1283, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 1290, 1291, 1292, 1293, 1294, 1294, 1295, 1296, 1297, 1298, 1299, 1300, \
    1301, 1302, 1303, 1304, 1305, 1305, 1306, 1307, 1308, 1309, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1317, 1318, \
    1319, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 1329, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, \
    1338, 1339, 1340, 1341, 1342, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 1350, 1351, 1352, 1353, 1354, 1355, 1356, \
    1356, 1357, 1358, 1359, 1360, 1361, 1362, 1363, 1364, 1365, 1366, 1367, 1368, 1369, 1370, 1370, 1371, 1372, 1373, 1374, \
    1375, 1376, 1377, 1378, 1379, 1380, 1381, 1382, 1383, 1384, 1385, 1385, 1386, 1387, 1388, 1389, 1390, 1391, 1392, 1393, \
    1394, 1395, 1396, 1397, 1398, 1399, 1400, 1401, 1401, 1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409, 1410, 1411, 1412, \
    1413, 1414, 1415, 1416, 1417, 1417, 1418, 1419, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 1430, 1431, \
    1432, 1433, 1434, 1435, 1435, 1436, 1437, 1438, 1439, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 1450, \
    1451, 1452, 1453, 1454, 1455, 1455, 1456, 1457, 1458, 1459, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, \
    1470, 1471, 1472, 1473, 1474, 1475, 1476, 1476, 1477, 1478, 1479, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, \
    1489, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 1500, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, \
    1508, 1509, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1526, \
    1527, 1528, 1529, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 1540, 1541, 1542, 1543, 1544, 1545, 1546, \
    1547, 1548, 1549, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1556, 1557, 1558, 1559, 1560, 1561, 1562, 1563, 1564, 1565, \
    1566, 1567, 1568, 1569, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 1580, 1581, 1582, 1583, 1584, 1585, \
    1586, 1587, 1588, 1589, 1590, 1591, 1592, 1592, 1593, 1594, 1595, 1596, 1597, 1598, 1599, 1600, 1601, 1602, 1603, 1604, \
    1605, 1606, 1607, 1608, 1609, 1610, 1611, 1612, 1613, 1614, 1615, 1616, 1617, 1618, 1619, 1620, 1621, 1622, 1623, 1624, \
    1625, 1626, 1627, 1628, 1629, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1637, 1638, 1639, 1640, 1641, 1642, 1643, \
    1644, 1645, 1646, 1647, 1648, 1649, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 1660, 1661, 1662, 1663, \
    1664, 1665, 1666, 1667, 1668, 1669, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 1680, 1681, 1682, 1683, \
    1684, 1685, 1686, 1687, 1688, 1689, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 1700, 1701, 1702, 1702, \
    1703, 1704, 1705, 1706, 1707, 1708, 1709, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 1720, 1721, 1722, \
    1723, 1724, 1725, 1726, 1727, 1728, 1729, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 1740, 1741, 1742, \
    1743, 1744, 1745, 1746, 1747, 1748, 1749, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 1760, 1761, 1762, \
    1763, 1764, 1765, 1766, 1767, 1768, 1769, 1770, 1771, 1772, 1773, 1774, 1775, 1776, 1777, 1778, 1779, 1780, 1781, 1782, \
    1783, 1784, 1785, 1786, 1787, 1788, 1789, 1790, 1791, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 1800, 1801, 1802, \
    1803, 1804, 1805, 1806, 1807, 1808, 1809, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 1820, 1821, 1822, \
    1823, 1824, 1825, 1826, 1827, 1828, 1829, 1830, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 1840, 1841, 1842, \
    1843, 1844, 1845, 1846, 1847, 1848, 1849, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 1860, 1861, 1862, \
    1863, 1864, 1865, 1866, 1867, 1868, 1869, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 1880, 1881, 1882, \
    1883, 1884, 1885, 1886, 1887, 1888, 1889, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 1900, 1901, 1902, \
    1903, 1904, 1905, 1906, 1907, 1908, 1909, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 1920, 1921, 1922, \
    1923, 1924, 1925, 1926, 1927, 1928, 1929, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 1940, 1941, 1942, \
    1943, 1944, 1945, 1946, 1947, 1948, 1949, 1950, 1951, 1952, 1953, 1954, 1955, 1955, 1956, 1957, 1958, 1959, 1960, 1961, \
    1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 1980, 1981, \
    1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, \
    2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, \
    2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029, 2030, 2031, 2032, 2033, 2034, 2035, 2036, 2037, 2038, 2039, 2040, 2041, \
    2042, 2043, 2044, 2045, 2046, 2047, 2048, 2049, 2050, 2051, 2052, 2053, 2054, 2055, 2056, 2057, 2058, 2059, 2060, 2061, \
    2062, 2063, 2064, 2065, 2066, 2067, 2068, 2069, 2070, 2071, 2072, 2073, 2074, 2075, 2076, 2077, 2078, 2079, 2080, 2081, \
    2082, 2083, 2084, 2085, 2086, 2087, 2088, 2089, 2090, 2091, 2092, 2093, 2094, 2095, 2096, 2097, 2098, 2099, 2100, 2101, \
    2102, 2103, 2104, 2105, 2106, 2107, 2108, 2109, 2110, 2111, 2112, 2113, 2114, 2115, 2116, 2117, 2118, 2119, 2120, 2121, \
    2122, 2123, 2124, 2125, 2126, 2127, 2128, 2129, 2130, 2131, 2132, 2133, 2134, 2135, 2136, 2137, 2138, 2139, 2140, 2141, \
    2142, 2143, 2144, 2145, 2146, 2147, 2148, 2149, 2150, 2151, 2152, 2153, 2154, 2155, 2156, 2157, 2158, 2159, 2160, 2161, \
    2162, 2163, 2164, 2165, 2166, 2167, 2168, 2169, 2170, 2171, 2172, 2173, 2174, 2175, 2176, 2177, 2178, 2179, 2180, 2181, \
    2182, 2183, 2184, 2185, 2186, 2187, 2188, 2189, 2190, 2191, 2192, 2193, 2194, 2195, 2196, 2197, 2198, 2199, 2200, 2201, \
    2202, 2203, 2204, 2205, 2205, 2206, 2207, 2208, 2209, 2210, 2211, 2212, 2213, 2214, 2215, 2216, 2217, 2218, 2219, 2220, \
    2221, 2222, 2223, 2224, 2225, 2226, 2227, 2228, 2229, 2230, 2231, 2232, 2233, 2234, 2235, 2236, 2237, 2238, 2239, 2240, \
    2241, 2242, 2243, 2244, 2245, 2246, 2247, 2248, 2249, 2250, 2251, 2252, 2253, 2254, 2255, 2256, 2257, 2258, 2259, 2260, \
    2261, 2262, 2263, 2264, 2265, 2266, 2267, 2268, 2269, 2270, 2270, 2271, 2272, 2273, 2274, 2275, 2276, 2277, 2278, 2279, \
    2280, 2281, 2282, 2283, 2284, 2285, 2286, 2287, 2288, 2289, 2290, 2291, 2292, 2293, 2294, 2295, 2296, 2297, 2298, 2299, \
    2300, 2301, 2302, 2303, 2304, 2305, 2306, 2307, 2308, 2309, 2310, 2311, 2312, 2313, 2314, 2315, 2315, 2316, 2317, 2318, \
    2319, 2320, 2321, 2322, 2323, 2324, 2325, 2326, 2327, 2328, 2329, 2330, 2331, 2332, 2333, 2334, 2335, 2336, 2337, 2338, \
    2339, 2340, 2341, 2342, 2343, 2344, 2345, 2346, 2347, 2348, 2349, 2350, 2351, 2351, 2352, 2353, 2354, 2355, 2356, 2357, \
    2358, 2359, 2360, 2361, 2362, 2363, 2364, 2365, 2366, 2367, 2368, 2369, 2370, 2371, 2372, 2373, 2374, 2375, 2376, 2377, \
    2378, 2379, 2380, 2381, 2381, 2382, 2383, 2384, 2385, 2386, 2387, 2388, 2389, 2390, 2391, 2392, 2393, 2394, 2395, 2396, \
    2397, 2398, 2399, 2400, 2401, 2402, 2403, 2404, 2405, 2406, 2407, 2407, 2408, 2409, 2410, 2411, 2412, 2413, 2414, 2415, \
    2416, 2417, 2418, 2419, 2420, 2421, 2422, 2423, 2424, 2425, 2426, 2427, 2428, 2429, 2430, 2431, 2431, 2432, 2433, 2434, \
    2435, 2436, 2437, 2438, 2439, 2440, 2441, 2442, 2443, 2444, 2445, 2446, 2447, 2448, 2449, 2450, 2451, 2452, 2452, 2453, \
    2454, 2455, 2456, 2457, 2458, 2459, 2460, 2461, 2462, 2463, 2464, 2465, 2466, 2467, 2468, 2469, 2470, 2471, 2472, 2472, \
    2473, 2474, 2475, 2476, 2477, 2478, 2479, 2480, 2481, 2482, 2483, 2484, 2485, 2486, 2487, 2488, 2489, 2490, 2490, 2491, \
    2492, 2493, 2494, 2495, 2496, 2497, 2498, 2499, 2500, 2501, 2502, 2503, 2504, 2505, 2506, 2506, 2507, 2508, 2509, 2510, \
    2511, 2512, 2513, 2514, 2515, 2516, 2517, 2518, 2519, 2520, 2521, 2522, 2522, 2523, 2524, 2525, 2526, 2527, 2528, 2529, \
    2530, 2531, 2532, 2533, 2534, 2535, 2536, 2537, 2537, 2538, 2539, 2540, 2541, 2542, 2543, 2544, 2545, 2546, 2547, 2548, \
    2549, 2550, 2551, 2551, 2552, 2553, 2554, 2555, 2556, 2557, 2558, 2559, 2560, 2561, 2562, 2563, 2564, 2565, 2565, 2566, \
    2567, 2568, 2569, 2570, 2571, 2572, 2573, 2574, 2575, 2576, 2577, 2578, 2578, 2579, 2580, 2581, 2582, 2583, 2584, 2585, \
    2586, 2587, 2588, 2589, 2590, 2590, 2591, 2592, 2593, 2594, 2595, 2596, 2597, 2598, 2599, 2600, 2601, 2602, 2602, 2603, \
    2604, 2605, 2606, 2607, 2608, 2609, 2610, 2611, 2612, 2613, 2613, 2614, 2615, 2616, 2617, 2618, 2619, 2620, 2621, 2622, \
    2623, 2624, 2624, 2625, 2626, 2627, 2628, 2629, 2630, 2631, 2632, 2633, 2634, 2634, 2635, 2636, 2637, 2638, 2639, 2640, \
    2641, 2642, 2643, 2644, 2644, 2645, 2646, 2647, 2648, 2649, 2650, 2651, 2652, 2653, 2654, 2654, 2655, 2656, 2657, 2658, \
    2659, 2660, 2661, 2662, 2663, 2664, 2664, 2665, 2666, 2667, 2668, 2669, 2670, 2671, 2672, 2673, 2673, 2674, 2675, 2676, \
    2677, 2678, 2679, 2680, 2681, 2682, 2682, 2683, 2684, 2685, 2686, 2687, 2688, 2689, 2690, 2691, 2691, 2692, 2693, 2694, \
    2695, 2696, 2697, 2698, 2699, 2699, 2700, 2701, 2702, 2703, 2704, 2705, 2706, 2707, 2708, 2708, 2709, 2710, 2711, 2712, \
    2713, 2714, 2715, 2716, 2716, 2717, 2718, 2719, 2720, 2721, 2722, 2723, 2724, 2724, 2725, 2726, 2727, 2728, 2729, 2730, \
    2731, 2731, 2732, 2733, 2734, 2735, 2736, 2737, 2738, 2739, 2739, 2740, 2741, 2742, 2743, 2744, 2745, 2746, 2746, 2747, \
    2748, 2749, 2750, 2751, 2752, 2753, 2754, 2754, 2755, 2756, 2757, 2758, 2759, 2760, 2761, 2761, 2762, 2763, 2764, 2765, \
    2766, 2767, 2768, 2768, 2769, 2770, 2771, 2772, 2773, 2774, 2774, 2775, 2776, 2777, 2778, 2779, 2780, 2781, 2781, 2782, \
    2783, 2784, 2785, 2786, 2787, 2788, 2788, 2789, 2790, 2791, 2792, 2793, 2794, 2794, 2795, 2796, 2797, 2798, 2799, 2800, \
    2800, 2801, 2802, 2803, 2804, 2805, 2806, 2807, 2807, 2808, 2809, 2810, 2811, 2812, 2813, 2813, 2814, 2815, 2816, 2817, \
    2818, 2819, 2819, 2820, 2821, 2822, 2823, 2824, 2825, 2825, 2826, 2827, 2828, 2829, 2830, 2830, 2831, 2832, 2833, 2834, \
    2835, 2836, 2836, 2837, 2838, 2839, 2840, 2841, 2842, 2842, 2843, 2844, 2845, 2846, 2847, 2847, 2848, 2849, 2850, 2851, \
    2852, 2853, 2853, 2854, 2855, 2856, 2857, 2858, 2858, 2859, 2860, 2861, 2862, 2863, 2863, 2864, 2865, 2866, 2867, 2868, \
    2869, 2869, 2870, 2871, 2872, 2873, 2874, 2874, 2875, 2876, 2877, 2878, 2879, 2879, 2880, 2881, 2882, 2883, 2884, 2884, \
    2885, 2886, 2887, 2888, 2889, 2889, 2890, 2891, 2892, 2893, 2894, 2894, 2895, 2896, 2897, 2898, 2899, 2899, 2900, 2901, \
    2902, 2903, 2903, 2904, 2905, 2906, 2907, 2908, 2908, 2909, 2910, 2911, 2912, 2913, 2913, 2914, 2915, 2916, 2917, 2917, \
    2918, 2919, 2920, 2921, 2922, 2922, 2923, 2924, 2925, 2926, 2926, 2927, 2928, 2929, 2930, 2931, 2931, 2932, 2933, 2934, \
    2935, 2935, 2936, 2937, 2938, 2939, 2939, 2940, 2941, 2942, 2943, 2944, 2944, 2945, 2946, 2947, 2948, 2948, 2949, 2950, \
    2951, 2952, 2952, 2953, 2954, 2955, 2956, 2956, 2957, 2958, 2959, 2960, 2960, 2961, 2962, 2963, 2964, 2964, 2965, 2966, \
    2967, 2968, 2968, 2969, 2970, 2971, 2972, 2972, 2973, 2974, 2975, 2976, 2976, 2977, 2978, 2979, 2980, 2980, 2981, 2982, \
    2983, 2984, 2984, 2985, 2986, 2987, 2988, 2988, 2989, 2990, 2991, 2992, 2992, 2993, 2994, 2995, 2996, 2996, 2997, 2998, \
    2999, 2999, 3000, 3001, 3002, 3003, 3003, 3004, 3005, 3006, 3007, 3007, 3008, 3009, 3010, 3010, 3011, 3012, 3013, 3014, \
    3014, 3015, 3016, 3017, 3017, 3018, 3019, 3020, 3021, 3021, 3022, 3023, 3024, 3024, 3025, 3026, 3027, 3028, 3028, 3029, \
    3030, 3031, 3031, 3032, 3033, 3034, 3035, 3035, 3036, 3037, 3038, 3038, 3039, 3040, 3041, 3041, 3042, 3043, 3044, 3045, \
    3045, 3046, 3047, 3048, 3048, 3049, 3050, 3051, 3051, 3052, 3053, 3054, 3054, 3055, 3056, 3057, 3058, 3058, 3059, 3060, \
    3061, 3061, 3062, 3063, 3064, 3064, 3065, 3066, 3067, 3067, 3068, 3069, 3070, 3070, 3071, 3072, 3073, 3073, 3074, 3075, \
    3076, 3076, 3077, 3078, 3079, 3079, 3080, 3081, 3082, 3082, 3083, 3084, 3085, 3085, 3086, 3087, 3088, 3088, 3089, 3090, \
    3091, 3091, 3092, 3093, 3094, 3094, 3095, 3096, 3097, 3097, 3098, 3099, 3100, 3100, 3101, 3102, 3103, 3103, 3104, 3105, \
    3106, 3106, 3107, 3108, 3109, 3109, 3110, 3111, 3111, 3112, 3113, 3114, 3114, 3115, 3116, 3117, 3117, 3118, 3119, 3120, \
    3120, 3121, 3122, 3122, 3123, 3124, 3125, 3125, 3126, 3127, 3128, 3128, 3129, 3130, 3130, 3131, 3132, 3133, 3133, 3134, \
    3135, 3136, 3136, 3137, 3138, 3138, 3139, 3140, 3141, 3141, 3142, 3143, 3144, 3144, 3145, 3146, 3146, 3147, 3148, 3149, \
    3149, 3150, 3151, 3151, 3152, 3153, 3154, 3154, 3155, 3156, 3156, 3157, 3158, 3159, 3159, 3160, 3161, 3161, 3162, 3163, \
    3164, 3164, 3165, 3166, 3166, 3167, 3168, 3169, 3169, 3170, 3171, 3171, 3172, 3173, 3173, 3174, 3175, 3176, 3176, 3177, \
    3178, 3178, 3179, 3180, 3181, 3181, 3182, 3183, 3183, 3184, 3185, 3185, 3186, 3187, 3188, 3188, 3189, 3190, 3190, 3191, \
    3192, 3192, 3193, 3194, 3194, 3195, 3196, 3197, 3197, 3198, 3199, 3199, 3200, 3201, 3201, 3202, 3203, 3203, 3204, 3205, \
    3206, 3206, 3207, 3208, 3208, 3209, 3210, 3210, 3211, 3212, 3212, 3213, 3214, 3214, 3215, 3216, 3217, 3217, 3218, 3219, \
    3219, 3220, 3221, 3221, 3222, 3223, 3223, 3224, 3225, 3225, 3226, 3227, 3227, 3228, 3229, 3229, 3230, 3231, 3231, 3232, \
    3233, 3233, 3234, 3235, 3236, 3236, 3237, 3238, 3238, 3239, 3240, 3240, 3241, 3242, 3242, 3243, 3244, 3244, 3245, 3246, \
    3246, 3247, 3248, 3248, 3249, 3250, 3250, 3251, 3252, 3252, 3253, 3254, 3254, 3255, 3256, 3256, 3257, 3258, 3258, 3259, \
    3260, 3260, 3261, 3261, 3262, 3263, 3263, 3264, 3265, 3265, 3266, 3267, 3267, 3268, 3269, 3269, 3270, 3271, 3271, 3272, \
    3273, 3273, 3274, 3275, 3275, 3276, 3277, 3277, 3278, 3278, 3279, 3280, 3280, 3281, 3282, 3282, 3283, 3284, 3284, 3285, \
    3286, 3286, 3287, 3288, 3288, 3289, 3289, 3290, 3291, 3291, 3292, 3293, 3293, 3294, 3295, 3295, 3296, 3297, 3297, 3298, \
    3298, 3299, 3300, 3300, 3301, 3302, 3302, 3303, 3304, 3304, 3305, 3305, 3306, 3307, 3307, 3308, 3309, 3309, 3310, 3310, \
    3311, 3312, 3312, 3313, 3314, 3314, 3315, 3316, 3316, 3317, 3317, 3318, 3319, 3319, 3320, 3321, 3321, 3322, 3322, 3323, \
    3324, 3324, 3325, 3325, 3326, 3327, 3327, 3328, 3329, 3329, 3330, 3330, 3331, 3332, 3332, 3333, 3334, 3334, 3335, 3335, \
    3336, 3337, 3337, 3338, 3338, 3339, 3340, 3340, 3341, 3342, 3342, 3343, 3343, 3344, 3345, 3345, 3346, 3346, 3347, 3348, \
    3348, 3349, 3349, 3350, 3351, 3351, 3352, 3352, 3353, 3354, 3354, 3355, 3356, 3356, 3357, 3357, 3358, 3359, 3359, 3360, \
    3360, 3361, 3362, 3362, 3363, 3363, 3364, 3365, 3365, 3366, 3366, 3367, 3368, 3368, 3369, 3369, 3370, 3370, 3371, 3372, \
    3372, 3373, 3373, 3374, 3375, 3375, 3376, 3376, 3377, 3378, 3378, 3379, 3379, 3380, 3381, 3381, 3382, 3382, 3383, 3383, \
    3384, 3385, 3385, 3386, 3386, 3387, 3388, 3388, 3389, 3389, 3390, 3390, 3391, 3392, 3392, 3393, 3393, 3394, 3395, 3395, \
    3396, 3396, 3397, 3397, 3398, 3399, 3399, 3400, 3400, 3401, 3401, 3402, 3403, 3403, 3404, 3404, 3405, 3405, 3406, 3407, \
    3407, 3408, 3408, 3409, 3409, 3410, 3411, 3411, 3412, 3412, 3413, 3413, 3414, 3415, 3415, 3416, 3416, 3417, 3417, 3418, \
    3419, 3419, 3420, 3420, 3421, 3421, 3422, 3422, 3423, 3424, 3424, 3425, 3425, 3426, 3426, 3427, 3427, 3428, 3429, 3429, \
    3430, 3430, 3431, 3431, 3432, 3432, 3433, 3434, 3434, 3435, 3435, 3436, 3436, 3437, 3437, 3438, 3439, 3439, 3440, 3440, \
    3441, 3441, 3442, 3442, 3443, 3443, 3444, 3445, 3445, 3446, 3446, 3447, 3447, 3448, 3448, 3449, 3449, 3450, 3451, 3451, \
    3452, 3452, 3453, 3453, 3454, 3454, 3455, 3455, 3456, 3457, 3457, 3458, 3458, 3459, 3459, 3460, 3460, 3461, 3461, 3462, \
    3462, 3463, 3463, 3464, 3465, 3465, 3466, 3466, 3467, 3467, 3468, 3468, 3469, 3469, 3470, 3470, 3471, 3471, 3472, 3472, \
    3473, 3474, 3474, 3475, 3475, 3476, 3476, 3477, 3477, 3478, 3478, 3479, 3479, 3480, 3480, 3481, 3481, 3482, 3482, 3483, \
    3483, 3484, 3484, 3485, 3486, 3486, 3487, 3487, 3488, 3488, 3489, 3489, 3490, 3490, 3491, 3491, 3492, 3492, 3493, 3493, \
    3494, 3494, 3495, 3495, 3496, 3496, 3497, 3497, 3498, 3498, 3499, 3499, 3500, 3500, 3501, 3501, 3502, 3502, 3503, 3503, \
    3504, 3504, 3505, 3505, 3506, 3506, 3507, 3507, 3508, 3508, 3509, 3509, 3510, 3510, 3511, 3511, 3512, 3512, 3513, 3513, \
    3514, 3514, 3515, 3515, 3516, 3516, 3517, 3517, 3518, 3518, 3519, 3519, 3520, 3520, 3521, 3521, 3522, 3522, 3523, 3523, \
    3524, 3524, 3525, 3525, 3526, 3526, 3527, 3527, 3528, 3528, 3529, 3529, 3530, 3530, 3531, 3531, 3532, 3532, 3533, 3533, \
    3534, 3534, 3535, 3535, 3536, 3536, 3536, 3537, 3537, 3538, 3538, 3539, 3539, 3540, 3540, 3541, 3541, 3542, 3542, 3543, \
    3543, 3544, 3544, 3545, 3545, 3546, 3546, 3546, 3547, 3547, 3548, 3548, 3549, 3549, 3550, 3550, 3551, 3551, 3552, 3552, \
    3553, 3553, 3554, 3554, 3554, 3555, 3555, 3556, 3556, 3557, 3557, 3558, 3558, 3559, 3559, 3560, 3560, 3561, 3561, 3561, \
    3562, 3562, 3563, 3563, 3564, 3564, 3565, 3565, 3566, 3566, 3567, 3567, 3567, 3568, 3568, 3569, 3569, 3570, 3570, 3571, \
    3571, 3572, 3572, 3572, 3573, 3573, 3574, 3574, 3575, 3575, 3576, 3576, 3577, 3577, 3577, 3578, 3578, 3579, 3579, 3580, \
    3580, 3581, 3581, 3581, 3582, 3582, 3583, 3583, 3584, 3584, 3585, 3585, 3585, 3586, 3586, 3587, 3587, 3588, 3588, 3589, \
    3589, 3589, 3590, 3590, 3591, 3591, 3592, 3592, 3593, 3593, 3593, 3594, 3594, 3595, 3595, 3596, 3596, 3596, 3597, 3597, \
    3598, 3598, 3599, 3599, 3600, 3600, 3600, 3601, 3601, 3602, 3602, 3603, 3603, 3603, 3604, 3604, 3605, 3605, 3606, 3606, \
    3606, 3607, 3607, 3608, 3608, 3609, 3609, 3609, 3610, 3610, 3611, 3611, 3611, 3612, 3612, 3613, 3613, 3614, 3614, 3614, \
    3615, 3615, 3616, 3616, 3617, 3617, 3617, 3618, 3618, 3619, 3619, 3619, 3620, 3620, 3621, 3621, 3622, 3622, 3622, 3623, \
    3623, 3624, 3624, 3624, 3625, 3625, 3626, 3626, 3627, 3627, 3627, 3628, 3628, 3629, 3629, 3629, 3630, 3630, 3631, 3631, \
    3631, 3632, 3632, 3633, 3633, 3633, 3634, 3634, 3635, 3635, 3635, 3636, 3636, 3637, 3637, 3637, 3638, 3638, 3639, 3639, \
    3639, 3640, 3640, 3641, 3641, 3641, 3642, 3642, 3643, 3643, 3643, 3644, 3644, 3645, 3645, 3645, 3646, 3646, 3647, 3647, \
    3647, 3648, 3648, 3649, 3649, 3649, 3650, 3650, 3651, 3651, 3651, 3652, 3652, 3653, 3653, 3653, 3654, 3654, 3654, 3655, \
    3655, 3656, 3656, 3656, 3657, 3657, 3658, 3658, 3658, 3659, 3659, 3659, 3660, 3660, 3661, 3661, 3661, 3662, 3662, 3663, \
    3663, 3663, 3664, 3664, 3664, 3665, 3665, 3666, 3666, 3666, 3667, 3667, 3667, 3668, 3668, 3669, 3669, 3669, 3670, 3670, \
    3670, 3671, 3671, 3672, 3672, 3672, 3673, 3673, 3673, 3674, 3674, 3675, 3675, 3675, 3676, 3676, 3676, 3677, 3677, 3678, \
    3678, 3678, 3679, 3679, 3679, 3680, 3680, 3680, 3681, 3681, 3682, 3682, 3682, 3683, 3683, 3683, 3684, 3684, 3684, 3685, \
    3685, 3686, 3686, 3686, 3687, 3687, 3687, 3688, 3688, 3688, 3689, 3689, 3690, 3690, 3690, 3691, 3691, 3691, 3692, 3692, \
    3692, 3693, 3693, 3693, 3694, 3694, 3694, 3695, 3695, 3696, 3696, 3696, 3697, 3697, 3697, 3698, 3698, 3698, 3699, 3699, \
    3699, 3700, 3700, 3700, 3701, 3701, 3701, 3702, 3702, 3703, 3703, 3703, 3704, 3704, 3704, 3705, 3705, 3705, 3706, 3706, \
    3706, 3707, 3707, 3707, 3708, 3708, 3708, 3709, 3709, 3709, 3710, 3710, 3710, 3711, 3711, 3711, 3712, 3712, 3712, 3713, \
    3713, 3713, 3714, 3714, 3714, 3715, 3715, 3715, 3716, 3716, 3716, 3717, 3717, 3717, 3718, 3718, 3718, 3719, 3719, 3719, \
    3720, 3720, 3720, 3721, 3721, 3721, 3722, 3722, 3722, 3723, 3723, 3723, 3724, 3724, 3724, 3725, 3725, 3725, 3726, 3726, \
    3726, 3727, 3727, 3727, 3728, 3728, 3728, 3729, 3729, 3729, 3730, 3730, 3730, 3731, 3731, 3731, 3731, 3732, 3732, 3732, \
    3733, 3733, 3733, 3734, 3734, 3734, 3735, 3735, 3735, 3736, 3736, 3736, 3737, 3737, 3737, 3738, 3738, 3738, 3738, 3739, \
    3739, 3739, 3740, 3740, 3740, 3741, 3741, 3741, 3742, 3742, 3742, 3743, 3743, 3743, 3743, 3744, 3744, 3744, 3745, 3745, \
    3745, 3746, 3746, 3746, 3747, 3747, 3747, 3747, 3748, 3748, 3748, 3749, 3749, 3749, 3750, 3750, 3750, 3750, 3751, 3751, \
    3751, 3752, 3752, 3752, 3753, 3753, 3753, 3753, 3754, 3754, 3754, 3755, 3755, 3755, 3756, 3756, 3756, 3756, 3757, 3757, \
    3757, 3758, 3758, 3758, 3759, 3759, 3759, 3759, 3760, 3760, 3760, 3761, 3761, 3761, 3761, 3762, 3762, 3762, 3763, 3763, \
    3763, 3763, 3764, 3764, 3764, 3765, 3765, 3765, 3766, 3766, 3766, 3766, 3767, 3767, 3767, 3768, 3768, 3768, 3768, 3769, \
    3769, 3769, 3770, 3770, 3770, 3770, 3771, 3771, 3771, 3771, 3772, 3772, 3772, 3773, 3773, 3773, 3773, 3774, 3774, 3774, \
    3775, 3775, 3775, 3775, 3776, 3776, 3776, 3777, 3777, 3777, 3777, 3778, 3778, 3778, 3778, 3779, 3779, 3779, 3780, 3780, \
    3780, 3780, 3781, 3781, 3781, 3781, 3782, 3782, 3782, 3783, 3783, 3783, 3783, 3784, 3784, 3784, 3784, 3785, 3785, 3785, \
    3786, 3786, 3786, 3786, 3787, 3787, 3787, 3787, 3788, 3788, 3788, 3788, 3789, 3789, 3789, 3790, 3790, 3790, 3790, 3791, \
    3791, 3791, 3791, 3792, 3792, 3792, 3792, 3793, 3793, 3793, 3793, 3794, 3794, 3794, 3794, 3795, 3795, 3795, 3796, 3796, \
    3796, 3796, 3797, 3797, 3797, 3797, 3798, 3798, 3798, 3798, 3799, 3799, 3799, 3799, 3800, 3800, 3800, 3800, 3801, 3801, \
    3801, 3801, 3802, 3802, 3802, 3802, 3803, 3803, 3803, 3803, 3804, 3804, 3804, 3804, 3805, 3805, 3805, 3805, 3806, 3806, \
    3806, 3806, 3807, 3807, 3807, 3807, 3808, 3808, 3808, 3808, 3809, 3809, 3809, 3809, 3810, 3810, 3810, 3810, 3811, 3811, \
    3811, 3811, 3812, 3812, 3812, 3812, 3812, 3813, 3813, 3813, 3813, 3814, 3814, 3814, 3814, 3815, 3815, 3815, 3815, 3816, \
    3816, 3816, 3816, 3817, 3817, 3817, 3817, 3818, 3818, 3818, 3818, 3818, 3819, 3819, 3819, 3819, 3820, 3820, 3820, 3820, \
    3821, 3821, 3821, 3821, 3821, 3822, 3822, 3822, 3822, 3823, 3823, 3823, 3823, 3824, 3824, 3824, 3824, 3824, 3825, 3825, \
    3825, 3825, 3826, 3826, 3826, 3826, 3827, 3827, 3827, 3827, 3827, 3828, 3828, 3828, 3828, 3829, 3829, 3829, 3829, 3829, \
    3830, 3830, 3830, 3830, 3831, 3831, 3831, 3831, 3831, 3832, 3832, 3832, 3832, 3833, 3833, 3833, 3833, 3833, 3834, 3834, \
    3834, 3834, 3835, 3835, 3835, 3835, 3835, 3836, 3836, 3836, 3836, 3836, 3837, 3837, 3837, 3837, 3838, 3838, 3838, 3838, \
    3838, 3839, 3839, 3839, 3839, 3839, 3840, 3840, 3840, 3840, 3841, 3841, 3841, 3841, 3841, 3842, 3842, 3842, 3842, 3842, \
    3843, 3843, 3843, 3843, 3843, 3844, 3844, 3844, 3844, 3844, 3845, 3845, 3845, 3845, 3846, 3846, 3846, 3846, 3846, 3847, \
    3847, 3847, 3847, 3847, 3848, 3848, 3848, 3848, 3848, 3849, 3849, 3849, 3849, 3849, 3850, 3850, 3850, 3850, 3850, 3851, \
    3851, 3851, 3851, 3851, 3852, 3852, 3852, 3852, 3852, 3853, 3853, 3853, 3853, 3853, 3854, 3854, 3854, 3854, 3854, 3855, \
    3855, 3855, 3855, 3855, 3856, 3856, 3856, 3856, 3856, 3857, 3857, 3857, 3857, 3857, 3857, 3858, 3858, 3858, 3858, 3858, \
    3859, 3859, 3859, 3859, 3859, 3860, 3860, 3860, 3860, 3860, 3861, 3861, 3861, 3861, 3861, 3861, 3862, 3862, 3862, 3862, \
    3862, 3863, 3863, 3863, 3863, 3863, 3864, 3864, 3864, 3864, 3864, 3864, 3865, 3865, 3865, 3865, 3865, 3866, 3866, 3866, \
    3866, 3866, 3867, 3867, 3867, 3867, 3867, 3867, 3868, 3868, 3868, 3868, 3868, 3868, 3869, 3869, 3869, 3869, 3869, 3870, \
    3870, 3870, 3870, 3870, 3870, 3871, 3871, 3871, 3871, 3871, 3872, 3872, 3872, 3872, 3872, 3872, 3873, 3873, 3873, 3873, \
    3873, 3873, 3874, 3874, 3874, 3874, 3874, 3875, 3875, 3875, 3875, 3875, 3875, 3876, 3876, 3876, 3876, 3876, 3876, 3877, \
    3877, 3877, 3877, 3877, 3877, 3878, 3878, 3878, 3878, 3878, 3878, 3879, 3879, 3879, 3879, 3879, 3879, 3880, 3880, 3880, \
    3880, 3880, 3880, 3881, 3881, 3881, 3881, 3881, 3881, 3882, 3882, 3882, 3882, 3882, 3882, 3883, 3883, 3883, 3883, 3883, \
    3883, 3884, 3884, 3884, 3884, 3884, 3884, 3885, 3885, 3885, 3885, 3885, 3885, 3886, 3886, 3886, 3886, 3886, 3886, 3887, \
    3887, 3887, 3887, 3887, 3887, 3887, 3888, 3888, 3888, 3888, 3888, 3888, 3889, 3889, 3889, 3889, 3889, 3889, 3890, 3890, \
    3890, 3890, 3890, 3890, 3890, 3891, 3891, 3891, 3891, 3891, 3891, 3892, 3892, 3892, 3892, 3892, 3892, 3892, 3893, 3893, \
    3893, 3893, 3893, 3893, 3894, 3894, 3894, 3894, 3894, 3894, 3894, 3895, 3895, 3895, 3895, 3895, 3895, 3895, 3896, 3896, \
    3896, 3896, 3896, 3896, 3897, 3897, 3897, 3897, 3897, 3897, 3897, 3898, 3898, 3898, 3898, 3898, 3898, 3898, 3899, 3899, \
    3899, 3899, 3899, 3899, 3899, 3900, 3900, 3900, 3900, 3900, 3900, 3900, 3901, 3901, 3901, 3901, 3901, 3901, 3901, 3902, \
    3902, 3902, 3902, 3902, 3902, 3902, 3903, 3903, 3903, 3903, 3903, 3903, 3903, 3904, 3904, 3904, 3904, 3904, 3904, 3904, \
    3905, 3905, 3905, 3905, 3905, 3905, 3905, 3906, 3906, 3906, 3906, 3906, 3906, 3906, 3906, 3907, 3907, 3907, 3907, 3907, \
    3907, 3907, 3908, 3908, 3908, 3908, 3908, 3908, 3908, 3908, 3909, 3909, 3909, 3909, 3909, 3909, 3909, 3910, 3910, 3910, \
    3910, 3910, 3910, 3910, 3910, 3911, 3911, 3911, 3911, 3911, 3911, 3911, 3912, 3912, 3912, 3912, 3912, 3912, 3912, 3912, \
    3913, 3913, 3913, 3913, 3913, 3913, 3913, 3913, 3914, 3914, 3914, 3914, 3914, 3914, 3914, 3914, 3915, 3915, 3915, 3915, \
    3915, 3915, 3915, 3915, 3916, 3916, 3916, 3916, 3916, 3916, 3916, 3916, 3917, 3917, 3917, 3917, 3917, 3917, 3917, 3917, \
    3918, 3918, 3918, 3918, 3918, 3918, 3918, 3918, 3919, 3919, 3919, 3919, 3919, 3919, 3919, 3919, 3919, 3920, 3920, 3920, \
    3920, 3920, 3920, 3920, 3920, 3921, 3921, 3921, 3921, 3921, 3921, 3921, 3921, 3922, 3922, 3922, 3922, 3922, 3922, 3922, \
    3922, 3922, 3923, 3923, 3923, 3923, 3923, 3923, 3923, 3923, 3923, 3924, 3924, 3924, 3924, 3924, 3924, 3924, 3924, 3925, \
    3925, 3925, 3925, 3925, 3925, 3925, 3925, 3925, 3926, 3926, 3926, 3926, 3926, 3926, 3926, 3926, 3926, 3927, 3927, 3927, \
    3927, 3927, 3927, 3927, 3927, 3927, 3928, 3928, 3928, 3928, 3928, 3928, 3928, 3928, 3928, 3929, 3929, 3929, 3929, 3929, \
    3929, 3929, 3929, 3929, 3929, 3930, 3930, 3930, 3930, 3930, 3930, 3930, 3930, 3930, 3931, 3931, 3931, 3931, 3931, 3931, \
    3931, 3931, 3931, 3931, 3932, 3932, 3932, 3932, 3932, 3932, 3932, 3932, 3932, 3933, 3933, 3933, 3933, 3933, 3933, 3933, \
    3933, 3933, 3933, 3934, 3934, 3934, 3934, 3934, 3934, 3934, 3934, 3934, 3934, 3935, 3935, 3935, 3935, 3935, 3935, 3935, \
    3935, 3935, 3935, 3936, 3936, 3936, 3936, 3936, 3936, 3936, 3936, 3936, 3936, 3937, 3937, 3937, 3937, 3937, 3937, 3937, \
    3937, 3937, 3937, 3938, 3938, 3938, 3938, 3938, 3938, 3938, 3938, 3938, 3938, 3938, 3939, 3939, 3939, 3939, 3939, 3939, \
    3939, 3939, 3939, 3939, 3940, 3940, 3940, 3940, 3940, 3940, 3940, 3940, 3940, 3940, 3940, 3941, 3941, 3941, 3941, 3941, \
    3941, 3941, 3941, 3941, 3941, 3941, 3942, 3942, 3942, 3942, 3942, 3942, 3942, 3942, 3942, 3942, 3942, 3943, 3943, 3943, \
    3943, 3943, 3943, 3943, 3943, 3943, 3943, 3943, 3944, 3944, 3944, 3944, 3944, 3944, 3944, 3944, 3944, 3944, 3944, 3945, \
    3945, 3945, 3945, 3945, 3945, 3945, 3945, 3945, 3945, 3945, 3945, 3946, 3946, 3946, 3946, 3946, 3946, 3946, 3946, 3946, \
    3946, 3946, 3947, 3947, 3947, 3947, 3947, 3947, 3947, 3947, 3947, 3947, 3947, 3947, 3948, 3948, 3948, 3948, 3948, 3948, \
    3948, 3948, 3948, 3948, 3948, 3948, 3949, 3949, 3949, 3949, 3949, 3949, 3949, 3949, 3949, 3949, 3949, 3949, 3949, 3950, \
    3950, 3950, 3950, 3950, 3950, 3950, 3950, 3950, 3950, 3950, 3950, 3951, 3951, 3951, 3951, 3951, 3951, 3951, 3951, 3951, \
    3951, 3951, 3951, 3951, 3952, 3952, 3952, 3952, 3952, 3952, 3952, 3952, 3952, 3952, 3952, 3952, 3952, 3953, 3953, 3953, \
    3953, 3953, 3953, 3953, 3953, 3953, 3953, 3953, 3953, 3953, 3954, 3954, 3954, 3954, 3954, 3954, 3954, 3954, 3954, 3954, \
    3954, 3954, 3954, 3955, 3955, 3955, 3955, 3955, 3955, 3955, 3955, 3955, 3955, 3955, 3955, 3955, 3955, 3956, 3956, 3956, \
    3956, 3956, 3956, 3956, 3956, 3956, 3956, 3956, 3956, 3956, 3956, 3957, 3957, 3957, 3957, 3957, 3957, 3957, 3957, 3957, \
    3957, 3957, 3957, 3957, 3957, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 3958, 3958, \
    3959, 3959, 3959, 3959, 3959, 3959, 3959, 3959, 3959, 3959, 3959, 3959, 3959, 3959, 3959, 3960, 3960, 3960, 3960, 3960, \
    3960, 3960, 3960, 3960, 3960, 3960, 3960, 3960, 3960, 3960, 3961, 3961, 3961, 3961, 3961, 3961, 3961, 3961, 3961, 3961, \
    3961, 3961, 3961, 3961, 3961, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 3962, 3962, \
    3962, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3964, 3964, 3964, \
    3964, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3965, 3965, 3965, 3965, 3965, 3965, \
    3965, 3965, 3965, 3965, 3965, 3965, 3965, 3965, 3965, 3965, 3965, 3966, 3966, 3966, 3966, 3966, 3966, 3966, 3966, 3966, \
    3966, 3966, 3966, 3966, 3966, 3966, 3966, 3966, 3967, 3967, 3967, 3967, 3967, 3967, 3967, 3967, 3967, 3967, 3967, 3967, \
    3967, 3967, 3967, 3967, 3967, 3967, 3968, 3968, 3968, 3968, 3968, 3968, 3968, 3968, 3968, 3968, 3968, 3968, 3968, 3968, \
    3968, 3968, 3968, 3968, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, 3969, \
    3969, 3969, 3969, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, 3970, \
    3970, 3970, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, 3971, \
    3971, 3971, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, 3972, \
    3972, 3972, 3972, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, 3973, \
    3973, 3973, 3973, 3973, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, 3974, \
    3974, 3974, 3974, 3974, 3974, 3974, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 3975, \
    3975, 3975, 3975, 3975, 3975, 3975, 3975, 3975, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, \
    3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3976, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, \
    3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3977, 3978, 3978, 3978, 3978, \
    3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, 3978, \
    3978, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, 3979, \
    3979, 3979, 3979, 3979, 3979, 3979, 3979, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, \
    3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3980, 3981, 3981, 3981, 3981, 3981, 3981, \
    3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3981, \
    3981, 3981, 3981, 3982, 3982, 3982, 3982, 3982, 3982, 3982, 3982, 3982, 3982, 3982, 3982, 3982, 3982, 3982, 3982, 3982, \
    3982, 3982, 3982, 3982, 3982, 3982, 3982, 3982, 3982, 3982, 3982, 3982, 3982, 3983, 3983, 3983, 3983, 3983, 3983, 3983, \
    3983, 3983, 3983, 3983, 3983, 3983, 3983, 3983, 3983, 3983, 3983, 3983, 3983, 3983, 3983, 3983, 3983, 3983, 3983, 3983, \
    3983, 3983, 3983, 3983, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, \
    3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3984, 3985, 3985, 3985, \
    3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, \
    3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, 3985, 3986, 3986, 3986, 3986, 3986, 3986, 3986, 3986, 3986, \
    3986, 3986, 3986, 3986, 3986, 3986, 3986, 3986, 3986, 3986, 3986, 3986, 3986, 3986, 3986, 3986, 3986, 3986, 3986, 3986, \
    3986, 3986, 3986, 3986, 3986, 3986, 3986, 3986, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, \
    3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, 3987, \
    3987, 3987, 3987, 3987, 3987, 3987, 3987, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, \
    3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, \
    3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, \
    3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, \
    3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3989, 3990, 3990, 3990, 3990, 3990, 3990, 3990, \
    3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, \
    3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, 3990, \
    3990, 3990, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, \
    3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, \
    3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3991, 3992, 3992, 3992, 3992, 3992, 3992, \
    3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, \
    3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, \
    3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3992, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, \
    3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, \
    3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, \
    3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3993, 3994, 3994, 3994, 3994, 3994, 3994, \
    3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, \
    3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, \
    3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, 3994, \
    3994, 3994, 3994, 3994, 3994, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, \
    3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, \
    3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, \
    3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, 3995, \
    3995, 3995, 3995, 3995, 3995, 3995, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, \
    3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, \
    3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, \
    3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, \
    3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3996, 3997, \
    3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, \
    3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, \
    3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, \
    3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, \
    3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, \
    3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3997, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, \
    3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, \
    3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, \
    3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, \
    3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, \
    3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, \
    3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, 3998, \
    3998, 3998, 3998, 3998, 3998, 3998, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, \
    3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, \
    3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, \
    3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, \
    3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, \
    3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, \
    3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, \
    3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, \
    3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, 3999, \
    3999, 3999, 3999, 3999, 3999, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, \
    4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, \
    4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, \
    4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, \
    4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, \
    4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, \
    4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, \
    4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, \
    4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, \
    4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, \
    4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, \
    4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, \
    4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, \
    4000 ])