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 Go (1.6) (judge verdict: Time Limit Exceeded)

package main

import (
	"fmt"
)

func main() {
	const nMax = 500000
	var a [nMax]int
	var s string
	var N, ans, flg int
	flg = -1
	ans = 0
	fmt.Scanf("%s", &s)
	N = len([]rune(s))
	for j := 0; flg == j-1; j++ {
		for i := 0; i < N+1; i++ {
			if j == 0 {
				if (i == N && s[i-1] == '>') || (i == 0 && s[i] == '<') || (i != N && s[i] == '<' && s[i-1] == '>') {
					a[i] = j
					flg = j
				}
			} else {
				if i != N && s[i] == '<' && a[i] == j-1 {
					a[i+1] = j
					flg = j
				}
				if i != N && s[i] == '>' && a[i+1] == j-1 {
					a[i] = j
					flg = j
				}
			}
		}
	}

	for i := 0; i < N+1; i++ {
		ans += a[i]
		//fmt.Printf("%d:%d\n", i, a[i])
	}
	fmt.Println(ans)
}