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: Accepted)

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ii = pair<ll, ll>;
#define mp make_pair
#define pb push_back
#define fi first
#define se second
const ll MOD = 1e9 + 7;
const ll N = 5e5 + 5;

string s;
ll ans;
ll a[N];

void solve() {
    cin >> s;
    for(ll i = 0; i < s.size(); i++) {
        if(s[i] == '<') a[i + 1] = a[i] + 1; 
    }
    for(ll i = s.size() - 1; i >= 0; i--) {
        if(s[i] == '>') 
            a[i] = max(a[i], a[i + 1] + 1);
    }
    ans = 0;
    for(ll i = 0; i <= s.size(); i++) {
        ans += a[i];
    }
    cout << ans << "\n";
}

int main() {
    
    ios_base::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    
    solve();
    
}