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;

int main()
{
	string S;
	cin >> S;

	int N = S.size();
	vector<int> zero;
	for( int i = 0; i < N; i++ ) {
		if( i == 0 ) {
			if( S[i] == '>' && S[i + 1] == '<' ) zero.push_back( i + 1 );
			else if( S[i] == '<' ) zero.push_back( i );
		}
		if( i == N - 1 ) {
			if( S[i] == '>' ) zero.push_back( i + 1 );
		}
		else {
			if( S[i] == '>' && S[i + 1] == '<' ) zero.push_back( i + 1 );
		}
	}
	vector<int> a( N + 1 );
	for( int i = 0; i < zero.size(); i++ ) {
		int z = zero[i];
		int n = 0;
		for( int j = z - 1; j >= 0; j-- ) {
			if( S[j] == '<' ) break;
			n++;
			a[j] = max( a[j], n );
		}
		n = 0;
		for( int j = z + 1; j < N + 1; j++ ) {
			if( S[j - 1] == '>' ) break;
			n++;
			a[j] = max( a[j], n );
		}
	}
	long long ans = 0;
	for( int i = 0; i < N + 1; i++ ) {
		ans += a[i];
	}

	cout << ans << endl;
}