Problem:
Score : 700 points

Problem Statement

There are N cats.
We number them from 1 through N.

Each of the cats wears a hat.
Cat i says: "there are exactly a_i different colors among the N - 1 hats worn by the cats except me."

Determine whether there exists a sequence of colors of the hats that is consistent with the remarks of the cats.

Constraints

2 ≤ N ≤ 10^5

1 ≤ a_i ≤ N-1

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print Yes if there exists a sequence of colors of the hats that is consistent with the remarks of the cats; print No otherwise.

Sample Input 1

3
1 2 2

Sample Output 1

Yes

For example, if cat 1, 2 and 3 wears red, blue and blue hats, respectively, it is consistent with the remarks of the cats.

Sample Input 2

3
1 1 2

Sample Output 2

No

From the remark of cat 1, we can see that cat 2 and 3 wear hats of the same color.
Also, from the remark of cat 2, we can see that cat 1 and 3 wear hats of the same color.
Therefore, cat 1 and 2 wear hats of the same color, which contradicts the remark of cat 3.

Sample Input 3

5
4 3 4 3 4

Sample Output 3

No

Sample Input 4

3
2 2 2

Sample Output 4

Yes

Sample Input 5

4
2 2 2 2

Sample Output 5

Yes

Sample Input 6

5
3 3 3 3 3

Sample Output 6

No

Solution in Go (1.6) (judge verdict: Accepted)

package main

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

func main() {
	var n int
	fmt.Scan(&n)
	a := make([]int, n);
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Split(bufio.ScanWords)
	min, max := n, 0
	for i := 0; i < n; i++ {
		scanner.Scan()
		a[i], _ = strconv.Atoi(scanner.Text())
		if a[i] < min {
			min = a[i]
		}
		if a[i] > max {
			max = a[i]
		}
	}
	
	if max - min == 0 {
		if max == n - 1 || 2 * max <= n {
			fmt.Println("Yes")
		} else {
			fmt.Println("No")
		}
	} else if max - min <= 1 {
		k := 0
		for i := 0; i < n; i++ {
			if a[i] == max - 1 {
				k++
			}
		}
		if max > k && 2 * (max - k) <= n - k {
			fmt.Println("Yes")
		} else {
			fmt.Println("No")
		}
	} else {
		fmt.Println("No")
	}
}