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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

console.log((args=>{
  const S = args.trim();
  const L = S.length;
  const T = Array(L+1).fill(0);
  for ( let i = 0; i < L; i++ ) {
    if ( S[i] === '<' ) {
      T[i+1] = Math.max( T[i+1], T[i] + 1 );
    }
    if ( S[L-i-1] === '>' ) {
      T[L-i-1] = Math.max( T[L-i-1], T[L-i] + 1 );
    }
  }
  return `${T.reduce((a,b)=>a+b)}`;
})(require('fs').readFileSync('/dev/stdin', 'utf8')));