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: Time Limit Exceeded)

#define _USE_MATH_DEFINES
#include <iostream>
#include <algorithm>
#include <queue>
#include <stack>
#include <deque>
#include <climits>
#include <string>
#include <vector>
#include <set>
#include <map>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
//#include <tuple>

#define INF INT_MAX>>1 
#define SIZE 100010
#define MOD 1000000007
#define rep(i, n) for(int i=0; i<(int)(n); i++)
#define rep2(i, from, to) for(int i=(from); i<(int)(to); i++)
#define ALL(obj) (obj).begin(), (obj).end()
#define LLPair pair<ll, ll>
#define vint vector<int>
#define vll vector<ll>
typedef long long ll;

using namespace std;

int main(void){
	string str; cin >> str;
	vint l(str.length()+10);
	vint r(str.length()+10);

	rep(i, str.length()){
		int count = 0;
		rep(i, str.length()){
			if(str[i] == '<') count++;
			else count = 0;
			l[i+1] = count;
		}
		count = 0;
		for(int i=str.size()-1; i>=0; i--){
			if(str[i] == '>') count++;
			else count = 0;
			r[i] = count;
		}
	}

	int ans = 0;
	rep(i, str.length()+1){
		ans += max(r[i], l[i]);
	}
	cout << ans << endl;
}