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>

using namespace std;

constexpr unsigned int MAX_N { 5000005 };

long long p[MAX_N];

int main()
{
    ios::sync_with_stdio(false);

    string s;
    cin >> s;

    int n = s.length() + 1;

    p[n] = s[n - 1] == '>' ? p[n - 1] + 1 : 0;
    for (int i = n - 1; i >= 0; --i)
    {
        p[i] = s[i] == '>' ? p[i + 1] + 1 : 0;
    }

    long long count = 0, sum = 0;
    for (int i = 0; i < n - 1; ++i)
    {
        if ((s[i] == '<' && p[i] < p[i + 1]) ||
            (s[i] == '>' && p[i] > p[i + 1]))
        {
            continue;
        }

        if (s[i] == '<') p[i + 1] = p[i] + 1; 
    }

    for (int i = 0; i < n; ++i)
    {
            sum += p[i];
    }
    cout << sum << endl;
    return 0;
}