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>
#pragma GCC optimize("Ofast")

using namespace std;

#define rep(i, a, b) for(ll i = a; i < ll(b); ++i)
#define trav(a, x) for(auto& a : x)
#define all(x) x.begin(), x.end()
#define sz(x) (ll)(x).size()
typedef long long ll;
typedef pair<ll, ll> pii;
typedef vector<ll> vi;

int main() {
    cin.sync_with_stdio(0); cin.tie(0);
    cin.exceptions(cin.failbit);
    string str;
    cin>>str;

    vi a(1,0);
    ll mn = 0;
    ll ind = 0;
    while(ind<sz(str)){
        ll numUp = 0;
        while(ind<sz(str)&&str[ind]=='<'){
            numUp++;
            ind++;
        }
        rep(i,1,numUp)
            a.push_back(i);

        ll numDown = 0;
        while(ind<sz(str)&&str[ind]=='>'){
            numDown++;
            ind++;
        }
        a.push_back(max(numDown,a.back()+1));
        rep(i,1,numDown+1)
            a.push_back(numDown-i);
    }
    //if(str[0]=='>') a[0] = a[1]+1;

    ll ans = 0;
    trav(ai,a){
        //cout<<ai<<" ";
        ans += ai;
    }
    //cout<<endl;

    cout<<ans<<endl;
}