Given is a string S of length N-1. Each character in S is `<` or `>`.

A sequence of N non-negative integers, a_1,a_2,\cdots,a_N, is said to be good when the following condition is satisfied for all i (1 \leq i \leq N-1):

* If S_i= `<`: a_i<a_{i+1}
* If S_i= `>`: a_i>a_{i+1}



Find the minimum possible sum of the elements of a good sequence of N non-negative integers.

Constraints

* 2 \leq N \leq 5 \times 10^5
* S is a string of length N-1 consisting of `<` and `>`.

Input

Input is given from Standard Input in the following format:


S


Output

Find the minimum possible sum of the elements of a good sequence of N non-negative integers.

Examples

Input

<>>


Output

3


Input

<>>><<><<<<<>>><


Output

28
#include <bits/stdc++.h>
using namespace std;
const int N = 500000 + 10;
char s[N];
int main(){
    scanf("%s",s);
    int n = strlen(s);
    long long ans = 0;
    for(int i=0;i<n;i++){
        int x = 0, y = 0;
        while(i+x<n&&s[i+x]=='<') x++;
        while(i+x+y<n&&s[i+x+y]=='>') y++;
        i += x + y - 1;
        if(x>y) swap(x,y);
        y++;
        ans += 1ll * x * (x-1) / 2 + 1ll * y * (y-1) / 2;
    }
    printf("%lld\n",ans);
}
