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;
using llong = long long;
using ldbl = long double;
using lpair = pair<llong, llong>;

#define ALL(x) x.begin(), x.end()

const llong inf = 1'000'000'000'000'007ll;
const llong mod = 1e9+7;

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

	llong ret = 0;
	llong before = 0;
	llong cnt = 1;
	for (int &&i = 1, &&n = s.size(); i < n; ++i) {
		if (s[i-1] == s[i]) {
			++cnt;
		} else {
			if (s[i-1] == '<') {
				ret += cnt * (cnt+1) / 2;
				before = cnt;
			} else {
				ret += cnt * (cnt-1) / 2;
				if (before < cnt) {
					ret += cnt - before;
				}
				before = 0;
			}

			cnt = 1;
		}
	}
	if (s.back() == '<') {
		ret += cnt * (cnt+1) / 2;
		before = cnt;
	} else {
		ret += cnt * (cnt-1) / 2;
		if (before < cnt) {
			ret += cnt - before;
		}
		before = 0;
	}

	cout << ret << endl;

	return 0;
}