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;
const int maxn = 1e6 + 10;
char s[maxn];
int n;
vector<int> v;
int a[maxn];
typedef long long ll;
ll sum;

void solve() {
	scanf("%s", s + 1);
	n = strlen(s + 1);
	s[n + 1] = '<';
	s[0] = '>';
	for (int i = 0; i <= n; ++i) {
		if (s[i] == '>' && s[i + 1] == '<') {
			a[i] = 1;
			v.push_back(i);
		}
	}
	for (auto id : v) {
		for (int i = id - 1; ~i; --i) {
			if (s[i + 1] == '>') {
				a[i] = max(a[i], a[i + 1] + 1);
			}
			else {break;}
		}
		for (int i = id + 1; i <= n; ++i) {
			if (s[i] == '<') {
				a[i] = max(a[i], a[i - 1] + 1);
			}
			else {break;}
		}
	}
	for (int i = 0; i <= n; ++i) {
		sum += a[i] - 1;
		//fprintf(stderr, "%d ", a[i] - 1);
	}
	printf("%lld\n", sum);
}
int main() {
	solve();

	return 0;
}