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: Wrong Answer)

import java.io.InputStream
import java.math.BigDecimal
import java.math.BigInteger

private val MOD = 1e9.toLong() + 7

val input = FastScanner()

fun main(args: Array<String>) = input.run {
    val n = nextInt()
    val a = nextInts(n)
    println(if (solve(a)) "Yes" else "No")
}

fun solve(a: IntArray): Boolean {
    val n = a.size
    if (a.all { it == n - 1 }) return true
    val min = a.min()!!
    val max = a.max()!!
    if (max - min > 1) return false
    val unique = a.count { it == max - 1 }
    if (n - unique < 2) return false
    val nonUnique = max - unique
    return 2 * nonUnique <= n - unique
}

fun String.toBigInteger() = BigInteger(this)
fun String.toBigDecimal() = BigDecimal(this)

class FastScanner(private val input: InputStream = System.`in`) {
    private val sb = StringBuilder()
    private val buffer = ByteArray(4096)
    private var pos = 0
    private var size = 0

    fun nextString(): String? {
        var c = skipWhitespace()
        if (c < 0) return null

        return sb.run {
            setLength(0)

            do {
                append(c.toChar())
                c = read()
            } while (c > ' '.toInt())

            toString()
        }
    }

    fun nextLine(): String? {
        var c = read()
        if (c < 0) return null

        return sb.run {
            setLength(0)

            while (c >= 0 && c != '\n'.toInt()) {
                append(c.toChar())
                c = read()
            }

            toString()
        }
    }

    fun nextLong(): Long {
        var c = skipWhitespace()

        val sign = if (c == '-'.toInt()) {
            c = read()
            -1
        } else 1

        var ans = 0L

        while (c > ' '.toInt()) {
            ans = ans * 10 + c - '0'.toInt()
            c = read()
        }

        return sign * ans
    }

    fun nextInt() = nextLong().toInt()
    fun nextDouble() = nextString()?.toDouble() ?: 0.0
    fun nextBigInteger(): BigInteger = nextString()?.toBigInteger() ?: BigInteger.ZERO
    fun nextBigDecimal(): BigDecimal = nextString()?.toBigDecimal() ?: BigDecimal.ZERO

    fun nextStrings(n: Int) = Array<String>(n) { nextString() ?: "" }
    fun nextInts(n: Int) = IntArray(n) { nextInt() }
    fun nextLongs(n: Int) = LongArray(n) { nextLong() }
    fun nextDoubles(n: Int) = DoubleArray(n) { nextDouble() }
    fun nextBigIntegers(n: Int) = Array<BigInteger>(n) { nextBigInteger() }
    fun nextBigDecimals(n: Int) = Array<BigDecimal>(n) { nextBigDecimal() }

    fun nextStrings(n: Int, m: Int) = Array(n) { nextStrings(m) }
    fun nextInts(n: Int, m: Int) = Array(n) { nextInts(m) }
    fun nextLongs(n: Int, m: Int) = Array(n) { nextLongs(m) }
    fun nextDoubles(n: Int, m: Int) = Array(n) { nextDoubles(m) }
    fun nextBigIntegers(n: Int, m: Int) = Array(n) { nextBigIntegers(m) }
    fun nextBigDecimals(n: Int, m: Int) = Array(n) { nextBigDecimals(m) }

    private fun skipWhitespace(): Int {
        while (true) {
            val c = read()
            if (c > ' '.toInt() || c < 0) return c
        }
    }

    private fun read(): Int {
        while (pos >= size) {
            if (size < 0) return -1
            size = input.read(buffer, 0, buffer.size)
            pos = 0
        }
        return buffer[pos++].toInt()
    }
}