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: Wrong Answer)

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long LL;
#define N 500000 + 5

int n, Go[N][3], Deg[N], Dp[N], q[N];
char s[N];
LL sum;

int main()
{
	scanf("%s", s);
	n = strlen(s);
	for (int i = 0; i < n - 1; i ++)
	{
		if (s[i + 1] == '<')
			Go[i][++ Go[i][0]] = i + 1, Deg[i + 1] ++;
		else Go[i + 1][++ Go[i + 1][0]] = i, Deg[i] ++;
	}
	int l = 1, r = 0;
	for (int i = 0; i < n; i ++)
		if (!Deg[i])
			q[++ r] = i;
	while (l <= r)
	{
		int z = q[l ++];
		for (int i = 1; i <= Go[z][0]; i ++)
		{
			int d = Go[z][i];
			Dp[d] = max(Dp[d], Dp[z] + 1), Deg[d] --;
			if (!Deg[d])
				q[++ r] = d;
		}
	}
	for (int i = 0; i < n; i ++)
		sum += Dp[i];
	printf("%lld\n", sum);
	return 0;
}