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.

Examples

Input

3
1 2 2


Output

Yes


Input

3
1 1 2


Output

No


Input

5
4 3 4 3 4


Output

No


Input

3
2 2 2


Output

Yes


Input

4
2 2 2 2


Output

Yes


Input

5
3 3 3 3 3


Output

No
#!/usr/bin/env python3

import sys, math, copy
# import fractions, itertools
# import numpy as np
# import scipy

HUGE = 2147483647
HUGEL = 9223372036854775807
ABC = "abcdefghijklmnopqrstuvwxyz"

def main():
    n = int(input())
    ai = list(map(int, input().split()))
    ma = max(ai)
    k = 0
    for a in ai:
        if a < ma - 1:
            return False
        if a == ma:
            k += 1

    if k == n:
        if ma + 1 == n:
            return True
        elif 1 <= ma <= n // 2:
            return True
        else:
            return False

    if k >= 2 and 1 <= ma - n + k <= k // 2:
        return True
    return False

print("Yes" if main() else "No")
