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: Wrong Answer)

S = input().strip()
V = []
for i in range(len(S)-1):
    if S[i]==">" and S[i+1]=="<":
        V.append(i+1)
if S[-1]==">":
    V.append(len(S))
B = [0 for _ in range(len(S)+1)]
for i in range(len(S)):
    if S[i]==">":
        B[i+1] = B[i]-1
    else:
        B[i+1] = B[i]+1
for j in V:
    if B[j]<0:
        B[j] = 0
        cur = j-1
        while cur>=0 and S[cur]==">":
            if cur>0:
                B[cur] = max(B[cur],B[cur+1]+1)
            cur -= 1
    elif B[j]>0:
        B[j] = 0
        cur = j-1
        while cur>=0 and S[cur]==">":
            if cur-1>=0 and S[cur-1]==">":
                B[cur] = B[cur+1]+1
            elif cur-1>=0 and S[cur-1]=="<":
                B[cur] = max(B[cur],B[cur+1]+1)
            cur -= 1
    cur = j
    while cur<len(S) and S[cur]=="<":
        B[cur+1] = B[cur]+1
        cur += 1
print(sum(B))