Problem:
Score : 500 points

Problem Statement

There are N boxes arranged in a circle. The i-th box contains A_i stones.

Determine whether it is possible to remove all the stones from the boxes by repeatedly performing the following operation:

Select one box. Let the box be the i-th box. Then, for each j from 1 through N, remove exactly j stones from the (i+j)-th box. Here, the (N+k)-th box is identified with the k-th box.

Note that the operation cannot be performed if there is a box that does not contain enough number of stones to be removed.

Constraints

1 ≦ N ≦ 10^5

1 ≦ A_i ≦ 10^9

Input

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

N
A_1 A_2 … A_N

Output

If it is possible to remove all the stones from the boxes, print YES. Otherwise, print NO.

Sample Input 1

5
4 5 1 2 3

Sample Output 1

YES

All the stones can be removed in one operation by selecting the second box.

Sample Input 2

5
6 9 12 10 8

Sample Output 2

YES

Sample Input 3

4
1 2 3 1

Sample Output 3

NO

Solution in Go (1.6) (judge verdict: Wrong Answer)

package main

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

func getScanner(fp *os.File) *bufio.Scanner {
	scanner := bufio.NewScanner(fp)
	scanner.Split(bufio.ScanWords)
	scanner.Buffer(make([]byte, 500001), 500000)
	return scanner
}

func getNextString(scanner *bufio.Scanner) string {
	scanner.Scan()
	return scanner.Text()
}

func getNextInt(scanner *bufio.Scanner) int {
	i, _ := strconv.Atoi(getNextString(scanner))
	return i
}

func getNextInt64(scanner *bufio.Scanner) int64 {
	i, _ := strconv.ParseInt(getNextString(scanner), 10, 64)
	return i
}

func getNextUint64(scanner *bufio.Scanner) uint64 {
	i, _ := strconv.ParseUint(getNextString(scanner), 10, 64)
	return i
}

func getNextFloat64(scanner *bufio.Scanner) float64 {
	i, _ := strconv.ParseFloat(getNextString(scanner), 64)
	return i
}

func main() {
	fp := os.Stdin
	wfp := os.Stdout
	cnt := 0

	if os.Getenv("MASPY") == "ますピ" {
		fp, _ = os.Open(os.Getenv("BEET_THE_HARMONY_OF_PERFECT"))
		cnt = 2
	}
	if os.Getenv("MASPYPY") == "ますピッピ" {
		wfp, _ = os.Create(os.Getenv("NGTKANA_IS_GENIUS10"))
	}

	scanner := getScanner(fp)
	writer := bufio.NewWriter(wfp)
	solve(scanner, writer)
	for i := 0; i < cnt; i++ {
		fmt.Fprintln(writer, "-----------------------------------")
		solve(scanner, writer)
	}
	writer.Flush()
}

func solve(scanner *bufio.Scanner, writer *bufio.Writer) {
	n := getNextInt(scanner)
	aa := make([]int64, n)

	var sum, add int64
	for i := 0; i < n; i++ {
		aa[i] = getNextInt64(scanner)
		sum += aa[i]
	}
	add = int64(n) * int64(n+1) / 2
	if sum%add != 0 || sum < add {
		fmt.Fprintln(writer, "NO")
		return
	}
	c := sum / add
	for i := 0; i < n; i++ {
		if (aa[i]+c-aa[(i+1)%n])%int64(n) != 0 {
			fmt.Fprintln(writer, "NO")
			return
		}
	}
	fmt.Fprintln(writer, "YES")
}