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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <string>
#include <vector>
#include <numeric>

using namespace std;

int main(int argc, char const *argv[])
{
    string S;
    cin >> S;
    vector<long long> a(S.size() + 1);
    vector<long long> b(S.size() + 1);
    vector<long long> c(S.size() + 1);

    for (int i = 0; i <= S.size() - 1; i++)
    {
        if (S[i] == '<') a[i + 1] = a[i] + 1;
    }

    for (int i = S.size() - 1; i >= 0; i--)
    {
        if (S[i] == '>') b[i] = b[i + 1] + 1;
    }
    
    for (int i = 0; i < c.size(); i++)
    {
        c[i] = max(a[i], b[i]);
    }
    
    cout << (long long)accumulate(c.begin(), c.end(), 0) << endl;
    
    return 0;
}