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 Python (3.4.3) (judge verdict: Accepted)

S=input()
N=len(S)
x=[-1]*(N+1)
M=[-1]*(N+1)
from collections import deque
l=deque()
m=2
for i in range(N-1):
    if S[i:i+2]=='><':
        l.append((i+1,0,m))
        m+=1
if S[0]=='<':
    l.append((0,0,0))
if S[-1]=='>':
    l.append((N,0,1))
while l:
    n,v,m=l.popleft()
    if x[n]<0:
        x[n]=v
        M[n]=m
        if n>0 and S[n-1]=='>':
            l.append((n-1,v+1,m))
        if n<N and S[n]=='<':
            l.append((n+1,v+1,m))
    elif M[n]!=m:
        x[n]=v
        M[n]=m
print(sum(x))