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;
typedef long long ll;
const int N=5e5+7;

ll ans;
char s[N];
int n,sl[N],sr[N];

int main()
{
    cin>>(s+1);
    n=strlen(s+1);
    for(int i=1;i<=n;i++){
        if(s[i]=='>') sl[i]=i;
        else sl[i]=sl[i-1];
    }
    sr[n]=n;
    for(int i=n-1;i>=0;i--){
        if(s[i+1]=='<') sr[i]=i;
        else sr[i]=sr[i+1];
    }
    for(int i=0;i<=n;i++)
        ans+=max(i-sl[i],sr[i]-i);
    cout<<ans<<endl;
    return 0;
}
