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 (GCC 5.4.1) (judge verdict: Accepted)

c,d,t,u,sz,n;
long s;
char x[18],buf[5<<17];
main()
{
	n=read(0,buf,5<<17);
	c=*buf;
	for(;++sz<n;)
	{
		++t;
		d=buf[sz];
		if(c!=d)
		{
			s+=(long)t*(t+1)>>1;
			if(c=='>')s-=t<u?t:u;
			u=t;
			t=0;
			c=d;
		}
	}
	t=17;
	do{
		x[--t]=s%10+'0';
		s/=10;
	}while(s);
	write(1,x+t,17-t);
}