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)

/*

    author : s@if

*/

#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using namespace std;

#define 		NIL 			-1
#define		 	fi	 		    first
#define 		sec 			second
#define 		MAX 			INT_MAX
#define			INF 			99999999
#define 		ll 			    long long
#define 		PI 			    acos(-1.0)
#define			MOD 			1000000007
#define 		PLL 			pair<ll,ll>
#define 		PII			    pair<int,int>
#define 		ull 			unsigned long long
#define 		For(i,a,b) 		for(int i=a;i<=(int)b;i++)
typedef tree<int, null_type, less<int>, rb_tree_tag,
            tree_order_statistics_node_update> new_data_set;

//*find_by_order(k)  gives the kth element;
//order_of_key(item)   gives the index(number of element strictly less than item) of item;


inline int in() {int x; scanf("%d", &x); return x; }
bool Check(int N , int pos)	{	return (bool) (N & (1<<pos));}
int Set(int N, int pos) {	return N = N | (1<<pos);}

int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};
int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};
int hr[]={-2,-2,-1,+1,+2,+2,-1,+1};
int hc[]={+1,-1,+2,+2,-1,+1,-2,-2};
int dx[]={+1,-1,+0,+0};
int dy[]={+0,+0,+1,-1};

const int MAXN = (int)1e5+9;

int main()
{
/*	freopen("input.txt","r",stdin);
    freopen("output.txt","w",stdout);
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);  */

    int i,j,k,l,m,n,p,q,x,y,u,v,r,tc,t;

    string s; cin>>s; n = s.size();

    int ara[n+9]; ara[n] = 0;

    for(i=n-1; i>=0; )
    {
        int cnt1 = 0, cnt2 = 0; j = i;

        while(j>=0 && s[j]=='>'){
            j--; cnt1++;
        }

        while(j>=0 && s[j]=='<'){
            j--; cnt2++;
        }

        k = i;

        for(p=k, q=1; q<cnt1; q++, p--)
            ara[p] = q;
        ara[p] = max(cnt1, cnt2); p--;

        for(q=1, v = cnt2-1; q<=cnt2; q++, p--)
        {
            ara[p] = v; v--;
        }

        i = j;
    }

    ll ans = 0;
    for(i=0; i<=n; i++){
       // cout<<ara[i]<<" ";
        ans+=ara[i];
    }

   // cout<<endl;

    cout<<ans<<endl;

  //  main();

    return 0;
}

// read the question correctly (is y a vowel? what are the exact constraints?)
// look out for SPECIAL CASES (n=1?) and overflow (ll vs int?)