import math

def compute_S_alpha(alpha):
    sum_val = 0.0
    j = 0
    while True:
        x_j = alpha + j
        if x_j == 0:
            term = 1.0
        else:
            term = (math.sin(x_j) / x_j) ** 2
        # Check if the term is too small to contribute
        if sum_val == 0.0:
            sum_val += term
            j += 1
            continue
        if term < 1e-16 * sum_val:
            break
        sum_val += term
        j += 1
    # Add tail approximation: 0.5 / (alpha + j)
    tail = 0.5 / (alpha + j)
    sum_val += tail
    return sum_val

def main():
    x = float(input().strip())
    if x.is_integer():
        result = (math.pi + 1) / 2
    else:
        m = math.floor(x)
        alpha = x - m
        sum_part = 0.0
        for k in range(m):
            x_k = alpha + k
            if x_k == 0:
                term = 1.0
            else:
                term = (math.sin(x_k) / x_k) ** 2
            sum_part += term
        S_alpha = compute_S_alpha(alpha)
        result = S_alpha - sum_part
    print("{0:.20f}".format(result))

if __name__ == '__main__':
    main()