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 <iostream>
#include <string>
#include <utility>
#include <algorithm>
#include <map>
#include <set>
#include <vector>
#include <cmath>
#include <cstdlib>
#include <queue>
#include <stack>
#include <iomanip>
#include <fstream>


using namespace std;

#define REP(i, n) for(ll i = 0;i < n;i++)
#define REPR(i, n) for(ll i = n;i >= 0;i--)
#define FOR(i, m, n) for(ll i = m;i < n;i++)
#define FORR(i, m, n) for(int i = m;i >= n;i--)
#define REPO(i, n) for(ll i = 1;i <= n;i++)
#define ll long long
#define INF (ll)1 << 60
#define MINF (-1 * INF)
#define ALL(n) n.begin(),n.end()
#define MOD (ll)1000000007
#define P pair<ll, ll>

string s;
ll now = 0, dp[510000], ans;

int main() {
	REP(i, 510000)dp[i] = -1;
	cin >> s;
	ll n = s.size();
	vector<P> t;
	REP(i, n + 1) {
		t.push_back(P(now, i + 1));
		if (i != n) {
			if (s[i] == '<')now++;
			else now--;
		}
	}
	sort(ALL(t));
	REP(i, t.size()) {
		dp[t[i].second] = max(dp[t[i].second - 1], dp[t[i].second + 1]) + 1;
	}
	REPO(i, n + 1) {
		ans += dp[i];
	//	cout << dp[i] << " ";
	}
	//cout << endl;
	cout << ans << endl;
}