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>
#define MAX 500010
using namespace std;

char str[MAX];
int arr[MAX];
vector<int> zero;

int main(void)
{
	cin >> str;
	int N = strlen(str);
	if (str[0] == '<') zero.push_back(0);
	for (int i = 1; i < N; i++)
	{
		if (str[i - 1] == '>' && str[i] == '<') zero.push_back(i);
	}
	if (str[N - 1] == '>') zero.push_back(N);
	for (int z : zero)
	{
		for (int i = z + 1; i <= N; i++)
		{
			arr[i] = arr[i - 1] + 1;
			if (str[i - 1] != str[i]) break;
		}
		for (int i = z - 1; arr[i] == 0; i--) arr[i] = arr[i + 1] + 1;
	}
	if (str[0] == '>' && !arr[0]) arr[0] = arr[1] + 1;
	if (str[N - 1] == '<' && !arr[N]) arr[N] = arr[N - 1] + 1;
	for (int i = 1; i < N; i++)
	{
		if (str[i - 1] == '<' && str[i] == '>') arr[i] = max(arr[i - 1], arr[i + 1]) + 1;
	}
	long long ans = 0;
	for (int i = 0; i <= N; i++) ans += arr[i];
	cout << ans << endl;
	return 0;
}