# 2014年ACM-ICPC西安邀请赛E题求大神解决

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Description

Professor Doge is now working on a project using polynomial for some mathematical calculations. In his project, he wants to approximate the exponential function e x with a polynomial whose degree does not exceed n. As one of professor’s assistants, you are asked to find a polynomial f (x) with degree n that minimizes

Input

There are several test cases, please process till EOF.
Each test case consists of only one integer denoting the degree n of the polynomial (0 ≤ n ≤ 10).

Output

For each test case, print n + 1 lines.
for the i-th line, print one floating number a i denoting the coefficient in the term x i, i = 0, 1, . . . , n.
It is guaranteed that the answer is always unique. Any answer within an absolute error less than or equal to 10 -50 would be accepted.

Sample Input

0 1

Sample Output

1.7182818284590452353602874713526624977572470936999595749 0.8731273138361809414411498854106499910289883747998382998 1.6903090292457285878382751718840250134565174378002425501

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1.先是运用数值分析中的最逼近完全平方式

2.解线性方程组

3.控制值的计算，用同余迭代法精确到50位

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