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>
typedef long long ll;
using namespace std;
#define FOR(i,a,b) for(ll i=(a);i<(b);i++)
#define REP(i,a) FOR(i,0,a)
const ll MAX_N=5e5;
ll N;
string S;
ll a[MAX_N];
ll dfs(ll i){
	if(a[i]!=-1){
		return a[i];
	}
	string s=S.substr(i,2);
	if(s=="<<"){
		a[i]=dfs(i-1)+1;
	}else if(s==">>"){
		a[i]=dfs(i+1)+1;
	}else if(s=="><"){
		a[i]=0;
	}else{
		a[i]=max(dfs(i-1),dfs(i+1))+1;
	}
	return a[i];
}
int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin>>S;
	N=S.size()+1;
	S='>'+S;
	S.push_back('<');
	memset(a,-1,sizeof(a));
	REP(i,N){
		dfs(i);
	}
	ll ans=0;
	REP(i,N){
		ans+=a[i];
	}
	cout<<ans<<endl;
}