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from decimal import *
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D = Decimal
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getcontext().prec = 100
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a = n = D(1)
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g, z, half = 1 / D(2).sqrt(), D(0.25), D(0.5)
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for i in range(18):
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x = [(a + g) * half, (a * g).sqrt()]
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var = x[0] - a
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z -= var * var * n
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n += n
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a, g = x
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print(a * a / z)
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