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: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
)

var sc = bufio.NewScanner(os.Stdin)

func main() {
	sc.Scan()
	input := sc.Text()
	fmt.Println(calc(input))
}

func calc(input string) int {

	var sum int
	numbers := make([]int, len(input)+1)

	for pos, r := range input {
		if r == '<' {
			numbers[pos+1] = numbers[pos] + 1
		} else { // >
			if numbers[pos]-1 >= 0 {
				numbers[pos+1] = 0
			} else {
				numbers[pos+1] = 0
				for i := pos; i > 0; i-- {
					numbers[i]++
					if numbers[i-1]-numbers[i] > 0 {
						break
					}
					if numbers[i] > numbers[i-1] {
						break
					}
				}
			}
		}
	}
	for _, n := range numbers {
		sum += n
	}
	return sum
}