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: Wrong Answer)

#include<bits/stdc++.h>
#define vll vector<ll>
#define vi vector<int>
#define vpll vector<pair<ll,ll>>
#define pii pair<int,int>
#define REP(i,a) for(int (i)=0; (i)<(a); (i)++)
#define RREP(i,a) for(int (i)=a-1; (i)>=(0); (i)--)
#define REP2(i,a,b) for(int (i)=(a); (i)<(b); (i)++)
#define MOD 1000000007
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define m0(x) memset(x,0,sizeof(x))
typedef long long ll;

using namespace std;

int main(){
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  string S; cin >> S;
  int N = S.size();
  vector<int> m;
  vector<int> a(N+1,0);
  for(int i=0;i<N;i++){
    if(S[i] == '<') a[i+1] = max(a[i] + 1, a[i+1]);
  }
  for(int i=N;i>0;i--){
    if(S[i] == '>') a[i] = max(a[i+1] + 1, a[i]);
  }
  
  int ans = 0;
  for(auto x : a){
    ans += x;
  }
  cout << ans;
  return 0;
}