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<bits/stdc++.h>
#define vll vector<ll>
#define vi vector<int>
#define vpll vector<pair<ll,ll>>
#define pii pair<int,int>
#define REP(i,a) for(int (i)=0; (i)<(a); (i)++)
#define RREP(i,a) for(int (i)=a-1; (i)>=(0); (i)--)
#define REP2(i,a,b) for(int (i)=(a); (i)<(b); (i)++)
#define MOD 1000000007
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define m0(x) memset(x,0,sizeof(x))
typedef long long ll;
using namespace std;

int main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	string s;cin>>s;
	int n=s.size()+1;
	vi a(n);
	REP(i,n-1) if(s[i]=='<') a[i+1] = max(a[i+1],a[i]+1);
	RREP(i,n-1) if(s[i]=='>') a[i] = max(a[i],a[i+1]+1);
	cout<<accumulate(ALL(a),int(0))<<endl;
  
    return 0;
}