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 (7.3.0) (judge verdict: Accepted)

s=input()
ans=0
a=[0]
for i in s:
  if i=='<':
    if a[-1]>=0:a[-1]+=1
    else:a+=[1]
  else:
    if a[-1]<0:a[-1]-=1
    else:a+=[-1]
n=len(a)
for i in range(n//2):
  i*=2
  j=i+1
  if a[i]<abs(a[j]):
    x=abs(a[j])
    y=a[i]-1
  else:
    x=abs(a[j])-1
    y=a[i]
  ans+=x*(x+1)//2+y*(y+1)//2
ans+=n%2*a[-1]*(a[-1]+1)//2
print(ans)