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: Wrong Answer)

#include<iostream>
#include<vector>
#include<string>
#include<map>
#include<algorithm>
#include<cmath>
using namespace std;

typedef long long int llint;

int height(int up,int down){
	if(up==0){
		return (down+1)*down/2;
	}else if(up>=down){
		return (up+1)*up/2+(down-1)*down/2;
	}else{
		return (up+(1+down-up))*up/2+down*down/2;
	}
}

int main(){
	string S;
	int up=0,down=0;
	bool climbing=true;
	int sum=0;
	cin >> S;
	for(const auto& c : S){
		if(c=='<'){
			if(climbing){
				up++;
			}else{
				climbing=true;
				sum+=height(up,down);
				up=1;
				down=0;
			}
		}else{
			climbing=false;
			down++;
		}
	}
	sum+=height(up,down);
	cout << sum << endl;
	return 0;
}