*【codeforces】数学期望

B. A Lot of Joy

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Two boys Gena and Petya wrote on two strips of paper the same string s that consisted of lowercase Latin letters. Then each boy took one strip, cut it into small pieces so that each piece contained exactly one letter and put all pieces into his pocket. After that Gena and Petya repeated the following procedure until their pockets became empty: they took one piece from their pockets and rejoiced if the letters on these pieces were equal.

Determine the expected number of times the boys rejoiced during this process.

Input

The input contains the only string s which was initially written on Gena's and Petya's strips. The string has length between1 and 200000, inclusively, and consists of lowercase Latin letters.

Output

Output the only real number — the expected number of times Gena and Petya rejoiced during their business. The absolute or relative error of the answer should not exceed10^- 9.

Examples

Input

abc

Output

1.000000000000000

Input

zzz

Output

3.000000000000000

题意：两个人分别拿一个纸条，写上相同的字符串，然后撕开，每一片纸上有一个字母，将碎片放进口袋，两人每次拿出一片，相同时，喜悦值+1，计算期望值

     每个字母出现概率累加和

code：

#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
int main()
{
	char s[200001];
	int a[200];
	while(~scanf("%s",s)){
		int l=strlen(s);
		memset(a,0,sizeof(a));
	for(int i=0;i<l;i++)
	a[s[i]-'a']++;//出现次数
	double sum=0.0;
	for(int i=0;i<l;i++)
	sum+=a[s[i]-'a']*1.0/l*1.0;	
	printf("%.15f\n",sum);
	}
	return 0;
 }