Favorite Dice 

BuggyD loves to carry his favorite die around. Perhaps you wonder why it's his favorite? Well, his die is magical and can be transformed into an N-sided unbiased die with the push of a button. Now BuggyD wants to learn more about his die, so he raises a question:

What is the expected number of throws of his die while it has N sides so that each number is rolled at least once?

Input

The first line of the input contains an integer t, the number of test cases. t test cases follow.

Each test case consists of a single line containing a single integer N (1 <= N <= 1000) - the number of sides on BuggyD's die.

Output

For each test case, print one line containing the expected number of times BuggyD needs to throw his N-sided die so that each number appears at least once. The expected number must be accurate to 2 decimal digits.

Example

Input:2112Output:1.0037.24

 

题意：

甩一个n面的骰子，问每一面都被甩到的次数期望是多少。

思路：

dp[i]:抛到i面的期望次数，dp[i]=dp[i-1]+n/(n-i+1)

代码：

1 #include"bits/stdc++.h" 2  3 #define db double 4 #define ll long long 5 #define vl vector
       
         6 #define ci(x) scanf("%d",&x) 7 #define cd(x) scanf("%lf",&x) 8 #define cl(x) scanf("%lld",&x) 9 #define pi(x) printf("%d\n",x)10 #define pd(x) printf("%f\n",x)11 #define pl(x) printf("%lld\n",x)12 #define rep(i, n) for(int i=0;i