import math


def logModel(x1, x2):
    if (x2 > math.log(x1)):
        return True
    else:
        return False


def circleModel(x1, x2):
    if ((x1-12.5)*(x1-12.5)+x2*x2<100 or (x1+12.5)*(x1+12.5)+x2*x2<100):
        return True
    else:
        return False


def polynomialModel(coefficientList,x,y):

    variableNum=len(coefficientList)
    output=0
    for i in range(variableNum):
        tmpList=coefficientList[i]
        tmpLength=len(tmpList)
        for j in range(tmpLength):
            power=tmpLength-j
                
            output+=tmpList[j]*math.pow(x[i],power)
    if (output>y):
        return True
    else:
        return False

def polycircleModel(center, radius, x):  
    # center format:[[0,1,3],[1,1,1]], radius format: [10,25], x format: [1,2,3]
    for i in range(len(center)):
        pointradius = 0
        for j in range(len(x)):
            pointradius += (x[j]-center[i][j])*(x[j]-center[i][j])
        if (pointradius < radius[i]*radius[i]):
            return True
    return False
238a75df37d5ddb35217640034d055b0ae7c4d54
<mask token>


def circleModel(x1, x2):
    if (x1 - 12.5) * (x1 - 12.5) + x2 * x2 < 100 or (x1 + 12.5) * (x1 + 12.5
        ) + x2 * x2 < 100:
        return True
    else:
        return False


<mask token>

<mask token>


def circleModel(x1, x2):
    if (x1 - 12.5) * (x1 - 12.5) + x2 * x2 < 100 or (x1 + 12.5) * (x1 + 12.5
        ) + x2 * x2 < 100:
        return True
    else:
        return False


<mask token>


def polycircleModel(center, radius, x):
    for i in range(len(center)):
        pointradius = 0
        for j in range(len(x)):
            pointradius += (x[j] - center[i][j]) * (x[j] - center[i][j])
        if pointradius < radius[i] * radius[i]:
            return True
    return False

<mask token>


def logModel(x1, x2):
    if x2 > math.log(x1):
        return True
    else:
        return False


def circleModel(x1, x2):
    if (x1 - 12.5) * (x1 - 12.5) + x2 * x2 < 100 or (x1 + 12.5) * (x1 + 12.5
        ) + x2 * x2 < 100:
        return True
    else:
        return False


def polynomialModel(coefficientList, x, y):
    variableNum = len(coefficientList)
    output = 0
    for i in range(variableNum):
        tmpList = coefficientList[i]
        tmpLength = len(tmpList)
        for j in range(tmpLength):
            power = tmpLength - j
            output += tmpList[j] * math.pow(x[i], power)
    if output > y:
        return True
    else:
        return False


def polycircleModel(center, radius, x):
    for i in range(len(center)):
        pointradius = 0
        for j in range(len(x)):
            pointradius += (x[j] - center[i][j]) * (x[j] - center[i][j])
        if pointradius < radius[i] * radius[i]:
            return True
    return False

import math


def logModel(x1, x2):
    if x2 > math.log(x1):
        return True
    else:
        return False


def circleModel(x1, x2):
    if (x1 - 12.5) * (x1 - 12.5) + x2 * x2 < 100 or (x1 + 12.5) * (x1 + 12.5
        ) + x2 * x2 < 100:
        return True
    else:
        return False


def polynomialModel(coefficientList, x, y):
    variableNum = len(coefficientList)
    output = 0
    for i in range(variableNum):
        tmpList = coefficientList[i]
        tmpLength = len(tmpList)
        for j in range(tmpLength):
            power = tmpLength - j
            output += tmpList[j] * math.pow(x[i], power)
    if output > y:
        return True
    else:
        return False


def polycircleModel(center, radius, x):
    for i in range(len(center)):
        pointradius = 0
        for j in range(len(x)):
            pointradius += (x[j] - center[i][j]) * (x[j] - center[i][j])
        if pointradius < radius[i] * radius[i]:
            return True
    return False

import math


def logModel(x1, x2):
    if (x2 > math.log(x1)):
        return True
    else:
        return False


def circleModel(x1, x2):
    if ((x1-12.5)*(x1-12.5)+x2*x2<100 or (x1+12.5)*(x1+12.5)+x2*x2<100):
        return True
    else:
        return False


def polynomialModel(coefficientList,x,y):

    variableNum=len(coefficientList)
    output=0
    for i in range(variableNum):
        tmpList=coefficientList[i]
        tmpLength=len(tmpList)
        for j in range(tmpLength):
            power=tmpLength-j
                
            output+=tmpList[j]*math.pow(x[i],power)
    if (output>y):
        return True
    else:
        return False

def polycircleModel(center, radius, x):  
    # center format:[[0,1,3],[1,1,1]], radius format: [10,25], x format: [1,2,3]
    for i in range(len(center)):
        pointradius = 0
        for j in range(len(x)):
            pointradius += (x[j]-center[i][j])*(x[j]-center[i][j])
        if (pointradius < radius[i]*radius[i]):
            return True
    return False