Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

<>>

Sample Output 1

3

a=(0,2,1,0) is a good sequence whose sum is 3.
There is no good sequence whose sum is less than 3.

Sample Input 2

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

Sample Output 2

28

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;

int main(){
  string S;
  cin >> S;
  int N = (int) S.size() + 1;
  vector<long long> A(N,0);
  for(int i=0;i<N-1;i++){
    if(S[i]=='<') A[i+1] = max(A[i+1],A[i]+1);
  }
  for(int i=N-1;i>=0;i--){
    if(S[i]=='>') A[i] = max(A[i],A[i+1]+1);
  }
  long long ans=0;
  for(int i=0;i<N;i++) ans += A[i];
  cout << ans << endl;
}