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 <iostream>
#include <cstdio>
#include <vector>
#include <cstring>
#include <bitset>
#include <cmath>
#include <iomanip>
#include <stack>
#include <set>
#include <queue>
#include <algorithm>
#include <deque>
#include <map>
#include <cmath>
#include <iomanip>
#include <numeric>
using namespace std;
 
#define INF 1e18
#define int long long
 
signed main() {
    string s; cin >> s;
    int n = s.size() + 1;
    vector<int> v(n, 0);
 
    int cnt1 = 0;
    for(int i = 0; i < n; i++) {
        if(s[i] == '<') {
            v[i] = cnt1;
            cnt1++;
        } else {
            v[i] = cnt1;
            cnt1 = 0;
        }
    }
 
    int cnt2 = 0;
    for(int i = n - 1; i >= 0; i--) {
        if(s[i] == '>') {
            cnt2++;
            v[i] = max(v[i], cnt2);
        } else {
            cnt2 = 0;
            v[i] = max(v[i], cnt2);
        }
    }
 
    int ans = 0;
    for(int i = 0; i < n; i++) {
        ans += v[i];
    }
    
    cout << ans << endl;;
    return 0;
}