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 Lua (5.3.2) (judge verdict: Wrong Answer)

s=io.read()
total=0
if s:sub(1,1)==">" then
    n=(#s:match(">"))
    total=total+n*(n+1)//2
end
if s:sub(#s,#s)=="<" then
    n=(#string.reverse(s):match("<+"))
    total=total+n*(n+1)//2
end
for i,_ in string.gmatch(s,"<+>+") do
    for j,_ in string.gmatch(i,">+") do
        x=math.max(#i-#j,#j)
        y=math.min(#i-#j,#j)
        total=total+x*(x+1)//2+y*(y-1)//2
    end
end
print(total)