Your task is to evaluate the following definite integral:
where P(x) = a_{4} · x^{4} + a_{3} · x^{3} + a_{2} · x^{2} + a_{1} · x + a_{0}. P(x) has no real roots and GCD(P(x), P'(x)) = const.
Input
The input contains five integers: a_{0}, a_{1}, a_{2}, a_{3} and a_{4} separated by whitespace. Each of these numbers does not exceed 10^{6} by absolute value, a_{4} ≠ 0.
Output
Output the value of the integral. Assume that the exact value is
A and your answer is
B. Your answer will be considered correct if and only if at least one of the following statements is true:
 A − 10^{−9} ≤ B ≤ A + 10^{−9}
 A · (1 − 10^{−9}) ≤ B ≤ A · (1 + 10^{−9})
Sample
input  output 

16 0 0 0 1  0.2776801836

Problem Source: SPbSU ITMO contest. Petrozavodsk training camp. Winter 2008.