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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.*
fun main(args: Array<String>){
	val cin = Scanner(System.`in`)
    val n = cin.nextInt()
    val a = Array<Int>(n, { cin.nextInt() })

    var t = a[0]
    var less = 0
    var same = 0
    var more = 0
    var ok = true

    for (i in 0..n-1) {
        if (a[i] == t + 1) {
            more += 1
        } else if (a[i] == t - 1) {
            less += 1
        } else if (a[i] == t) {
            same += 1
        } else {
            ok = false
            break
        }
    }

    var major = t
    var key = t
    
    var major_cats = same
    var key_cats = same

    if (more == 0) {
        key = t - 1
        key_cats = less
    } else if (less == 0) {
        major = t + 1
        major_cats = more
    } else {
        ok = false
    }

    if (more == 0 && less == 0) {
        major = t
        key = t        
    } 

    if (major != key) {
        val ex = major - key_cats
        if (0 >= ex || ex*2 > major_cats) {
            ok = false
        }
    } else {
        if (major != n - 1 && major*2 > n) {
            ok = false
        }
    }

    if (ok == false) {
        println("No")
    } else {
        println("Yes")
    }
}