Problem Statement

You are given a string S of length N-1 consisting of < and >.
$A sequence x=(x_1,x_2,\cdots,x_N)$ of length N is called a good sequence if and only if it satisfies the following condition:

• For each $i (1 \leq i \leq N-1)$, if the i-th character of S is <, then $x_i\lt x_{i+1}$; if it is >, then $x_i \gt x_{i+1}$.

Find the minimum possible inversion number of a good sequence.
What is the inversion number of a sequence?

The inversion number of $a sequence x=(x_1,x_2,\cdots,x_n)$ of length n is the number of pairs of integers $(i,j) (1 \leq i < j \leq n)$ such that x_i>x_j.

Input

The input is given from Standard Input in the following format:
N
S

Output

Print the answer.

Constraints

• $2 \leq N \leq 250000$
• S is a string of length N-1 consisting of < and >.
• All input values are integers.

Sample Input 1

4
<><

Sample Output 1

1

x=(1,2,1,2) is a good sequence, and its inversion number is 1.
There is no good sequence whose inversion number is 0, so the answer is 1.

Sample Input 2

2
<

Sample Output 2

0

Sample Input 3

10

Sample Output 3

45

Sample Input 4

30
<<><>>><><>><><><<>><<<><><<>

Sample Output 4

19

见题面 Input 部分

见题面 Output 部分