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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
int main(){
  cout << fixed << setprecision(20);
  string s;
  cin >> s;
  int64_t n=s.size()+1;
  vector<int64_t> k(n);
  for(int64_t i=0;i<n-1;i++)if(s[i]=='<')if(k[i+1]<k[i]+1)k[i+1]=k[i]+1;
  for(int64_t i=n-2;i>=0;i--)if(s[i]=='>')if(k[i]<k[i+1]+1)k[i]=k[i+1]+1;
  cout << accumulate(k.begin(),k.end(),int(0)) << endl;
}