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: Wrong Answer)

s = input()
n = len(s)+1
lsfg = [0]*n
flag = 0
ans = 0

for i in range(n-2):
    if s[i] != s[i+1]:
        flag += 1
        if s[i] == "<":
            lsfg[i+1] = -2
        else:
            lsfg[i+1] = -1

if flag == 0:
    p = 0
    for i in range(n):
        ans += p
        p += 1
else:
    for i in range(n):
        k = 0
        j = 0
        if lsfg[i] == -1:
            while i-k > 0:
                k += 1
                if lsfg[i-k] != -2:
                    lsfg[i-k] = k
                else:
                    break
            while i+j < n-1:
                j += 1
                if lsfg[i+j] != -2:
                    lsfg[i+j] = j
                else:
                    break

    lsfg = [0] + lsfg + [0]

    for i in range(n):
        if lsfg[i+1] == -2:
            if lsfg[i] > lsfg[i+2]:
                lsfg[i+1] = lsfg[i] +1
            else:
                lsfg[i+1] = lsfg[i+2] +1
        elif lsfg[i+1] == -1:
            lsfg[i+1] = 0

    ans = sum(lsfg)
    
print(ans)