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 PyPy3 (2.4.0) (judge verdict: Accepted)

from collections import Counter,defaultdict,deque
import sys
import bisect
import math
import itertools
import string
import queue
import copy
from heapq import heappop, heappush
input = sys.stdin.readline
sys.setrecursionlimit(10**8)
mod = 10**9+7

def inp(): # n=1
    return int(input())
def inpm(): # x=1,y=2
    return map(int,input().split())
def inpl(): # a=[1,2,3,4,5,...,n]
    return list(map(int, input().split()))
def inpls(): # a=['1','2','3',...,'n']
    return list(input().split())
def inplm(n): # x=[] 複数行
    return list(int(input()) for _ in range(n))
def inpll(n): # [[1,1,1,1],[2,2,2,2],[3,3,3,3]]
    return sorted([list(map(int, input().split())) for _ in range(n)])
def sortx(x,n,k):
    if k == 0:x.sort(key=lambda y:y[1,n])
    else:x.sort(reversed=True, key=lambda y:y[1,n])
def graph():
    n=inp()
    g=[[] for _ in range(n)]
    for i in range(n):
        a=inp()
        a-=1
        g[i].append(a)
        g[a].append(i)
    return n,g
def graphm():
    n,m=inpm()
    g=[[] for _ in range(n)]
    for _ in range(m):
        a,b,w=inpm()
        a-=1
        b-=1
        g[a].append((b,w))
        g[b].append((a,w))
    return n,m,g

def dijkstra(s,n,g): # sからの最短距離 頂点数n
    s -= 1
    que = []
    d = [10**15 for _ in range(n)]
    d[s] = 0
    heappush( que,(0,s) )
    while len(que)>0:
        p =  heappop(que)
        v = p[1]
        if d[v] < p[0]:
            continue
        for i in range(len(g[v])):
            edge = g[v][i]
            if d[edge[0]] > d[v] + edge[1]:
                d[edge[0]] = d[v] + edge[1]
                heappush( que,(d[edge[0]] , edge[0]) )
    return d

def main():
    n=inp()
    a=inpl()
    a.sort()
    if a[n-1]-a[0]>1 or a[n-1]>=n or a[0]<1:
        print("No")
        return
    cnt=1
    for i in range(n-1):
        if a[i+1]==a[i]:
            cnt+=1
        else:
            break
    if cnt==n:
        if a[0]==n-1 or n//a[n-1]>=2:
            print("Yes")
            return
        else:
            print("No")
            return
    if cnt>a[0]:
        print("No")
        return
    if (a[n-1]-(n%a[n-1]))>cnt:        
        print("No")
        return
    print("Yes")    


if __name__ == "__main__":
    main()