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;
#define long long
const int maxm=5e5+5;
vector<int>g[maxm];
char s[maxm];
int in[maxm];
int d[maxm];
int n;
signed main(){
    scanf("%s",s+1);
    n=strlen(s+1);
    n++;
    for(int i=1;i<=n-1;i++){
        if(s[i]=='>'){
            g[i+1].push_back(i);
            in[i]++;
        }else{
            g[i].push_back(i+1);
            in[i+1]++;
        }
    }
    queue<int>q;
    for(int i=1;i<=n;i++){
        if(in[i]==0){
            q.push(i);
        }
    }
    int ans=0;
    while(!q.empty()){
        int x=q.front();q.pop();
        ans+=d[x];
        for(int v:g[x]){
            if(in[v]){
                in[v]--;
                d[v]=max(d[v],d[x]+1);
                if(!in[v]){
                    q.push(v);
                }
            }
        }
    }
    cout<<ans<<endl;
    return 0;
}
/*

*/