import sys
f = open('q2input.txt', 'r')
sys.stdin = f

# Setup
import sys
sys.setrecursionlimit(4100000)

class Q2:
    def __init__(self):
        # Setup
        import sys
        sys.setrecursionlimit(4100000)


if __name__ == '__main__':
    q2 = Q2()
87295c6587c08fdd0806eb7543ebcfecb42a3e2e
<mask token>


class Q2:

    def __init__(self):
        import sys
        sys.setrecursionlimit(4100000)


<mask token>

<mask token>
sys.setrecursionlimit(4100000)


class Q2:

    def __init__(self):
        import sys
        sys.setrecursionlimit(4100000)


if __name__ == '__main__':
    q2 = Q2()

<mask token>
f = open('q2input.txt', 'r')
sys.stdin = f
<mask token>
sys.setrecursionlimit(4100000)


class Q2:

    def __init__(self):
        import sys
        sys.setrecursionlimit(4100000)


if __name__ == '__main__':
    q2 = Q2()

import sys
f = open('q2input.txt', 'r')
sys.stdin = f
import sys
sys.setrecursionlimit(4100000)


class Q2:

    def __init__(self):
        import sys
        sys.setrecursionlimit(4100000)


if __name__ == '__main__':
    q2 = Q2()

import sys
f = open('q2input.txt', 'r')
sys.stdin = f

# Setup
import sys
sys.setrecursionlimit(4100000)

class Q2:
    def __init__(self):
        # Setup
        import sys
        sys.setrecursionlimit(4100000)


if __name__ == '__main__':
    q2 = Q2()