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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>

int main(void) {

  char s[500001];
  scanf("%s", s);
  long length = strlen(s);
  long a[length+1];
  for (long i = 0; i < length+1; i++) {
    a[i] = -1;
  }
  if (s[0] == '<') {
    a[0] = 0;
  }
  for (long i = 1; i < length; i++) {
    if (s[i-1] == '>' && s[i] == '<') {
      a[i] = 0;
    }
    if (s[i-1] == '<' && s[i] == '<') {
      a[i] = a[i-1]+1;
    }
  }
  if (s[length-1] == '<') {
    a[length] = a[length-1]+1;
  } else {
    a[length] = 0;
  }
  for (long i = length-1; i >= 0; i--) {
    if (a[i] == -1) {
      a[i] = a[i+1]+1;
      if (a[i] <= a[i-1] && i != 0) {
        a[i] = a[i-1]+1;
      }
    }
  }
  long sum = 0;
  for (long i = 0; i < length+1; i++) {
    sum += a[i];
  }
  printf("%ld\n", sum);

  return 0;
}