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 PyPy3 (2.4.0) (judge verdict: Accepted)

S = input()
n = len(S)+1
a = [0] * n
for i in range(n-1):
	if(S[i] == '<'):
		if(a[i+1] < a[i]+1):
			a[i+1] = a[i]+1
for i in reversed(range(n-1)):
	if(S[i] == '>'):
		if(a[i] < a[i+1]+1):
			a[i] = a[i+1]+1
print(sum(a))