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

a=[0]
temp=0
f=0
mx_idx=0

for i in range(1,N):
    if S[i-1]=="<":
        if f>=0: 
            a.append(a[i-1]+1)
            temp+=1
            f=1
        else: 
            if temp>0:
                for j in range(mx_idx+1,i):
                    a[j]-=temp
            elif temp<0:
                for j in range(mx_idx,i):
                    a[j]-=temp
            a.append(1)
            temp=1
            f=1
    else:
        if f<=0:
            a.append(a[i-1]-1)
            temp-=1
        else: 
            a.append(a[i-1]-1)
            temp-=1
            mx_idx=i-1
            f=-1

if temp<0:
    for j in range(mx_idx, N):
        a[j] -= temp
print(sum(a))