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;

typedef long long LL;

const int N = 5e5 + 10;

int n, lft[N], rgt[N];
char s[N];

LL cal(LL x){
	return x * (x + 1) / 2;
}

int main(){
	scanf("%s", s);
	n = strlen(s);

	lft[0] = 0;
	for(int i=0; i<n; i++){
		if(s[i] == '<'){
			lft[i+1] = lft[i] + 1;
		} else {
			lft[i+1] = 0;
		}
	}

	rgt[n] = 0;
	for(int i=n-1; i>=0; i--){
		if(s[i] == '>'){
			rgt[i] = rgt[i+1] + 1;
		} else {
			rgt[i] = 0;
		}
	}

	LL ans = 0;
	
	for(int i=1; i<n; i++){
		if(lft[i] && rgt[i]){
			ans = ans + cal(lft[i]-1) + cal(rgt[i]-1) + max(lft[i], rgt[i]);
		}
	}

	ans = ans + cal(lft[n]) + cal(rgt[0]);

	printf("%lld\n", ans);

	return 0;
}