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: Time Limit Exceeded)

S = input()
N = len(S) + 1

la = [0] * N

cnt0 = 0
if S[0] == ">":
    cnt0 += 1
    j = 1
    while j <= len(S)-1 and S[j] == ">":
        cnt0 += 1
        j += 1
la[0] = cnt0

for i in range(1, N-1):
    j = i-1
    k = i+1
    cnt1 = 0
    cnt2 = 0
    if S[i-1] == "<" and i >= 0:
        while j >= 0 and S[j] == S[i-1] :
            cnt1 += 1 
            j -= 1
    if S[i] == ">":
        while k <= N-1 and S[i] == S[k-1]:
            cnt2 += 1
            k += 1 
    la[i] = max(cnt1, cnt2)

cntn = 0
if S[-1] == "<":
    cntn += 1
    j = -2
    while j >= -len(S) and S[j] == "<":
        cntn += 1
        j -= 1
la[-1] = cntn

print(sum(la))