Everybody knows what an arithmetic progression is. Let us remind you just in case that an arithmetic progression is such sequence of numbers a1, a2, ..., an of length n, that the following condition fulfills: 

a2 - a1 = a3 - a2 = a4 - a3 = ... = ai + 1 - ai = ... = an - an - 1.

For example, sequences [1, 5], [10], [5, 4, 3] are arithmetic progressions and sequences [1, 3, 2], [1, 2, 4] are not.

Alexander has n cards containing integers. Arthur wants to give Alexander exactly one more card with a number so that he could use the resulting n + 1 cards to make an arithmetic progression (Alexander has to use all of his cards).

Arthur has already bought a card but he hasn't written a number on it. Help him, print all integers that you can write on a card so that the described condition fulfilled.

Input

The first line contains integer n (1 ≤ n ≤ 105) — the number of cards. The next line contains the sequence of integers — the numbers on Alexander's cards. The numbers are positive integers, each of them doesn't exceed 108.

Output

If Arthur can write infinitely many distinct integers on the card, print on a single line -1.

Otherwise, print on the first line the number of integers that suit you. In the second line, print the numbers in the increasing order. Note that the numbers in the answer can exceed 108 or even be negative (see test samples).

Examples

Input

3
4 1 7


Output

2
-2 10


Input

1
10


Output

-1


Input

4
1 3 5 9


Output

1
7


Input

4
4 3 4 5


Output

0


Input

2
2 4


Output

3
0 3 6
import time,math,bisect,sys
from sys import stdin,stdout
from collections import deque
from fractions import Fraction
from collections import Counter
from collections import OrderedDict
pi=3.14159265358979323846264338327950
def II(): # to take integer input
    return int(stdin.readline())
def IO(): # to take string input
    return stdin.readline()
def IP(): # to take tuple as input
    return map(int,stdin.readline().split())
def L(): # to take list as input
    return list(map(int,stdin.readline().split()))
def P(x): # to print integer,list,string etc..
    return stdout.write(str(x))
def PI(x,y): # to print tuple separatedly
    return stdout.write(str(x)+" "+str(y)+"\n")
def lcm(a,b): # to calculate lcm
    return (a*b)//gcd(a,b)
def gcd(a,b): # to calculate gcd
    if a==0:
        return b
    elif b==0:
        return a
    if a>b:
        return gcd(a%b,b)
    else:
        return gcd(a,b%a)
def sieve():
    li=[True]*1000001
    li[0],li[1]=False,False
    for i in range(2,len(li),1):
        if li[i]==True:
            for j in range(i*i,len(li),i):
                li[j]=False
    prime=[]
    for i in range(1000001):
        if li[i]==True:
            prime.append(i)
    return prime
def setBit(n):
    count=0
    while n!=0:
        n=n&(n-1)
        count+=1
    return count
def readTree(v,e): # to read tree
    adj=[set() for i in range(v+1)]
    for i in range(e):
        u1,u2,w=IP()
        adj[u1].add((u2,w))
        adj[u2].add((u1,w))
    return adj
def dfshelper(adj,i,visited):
    nodes=1
    visited[i]=True
    for ele in adj[i]:
        if visited[ele]==False:
            nd=dfshelper(adj,ele,visited)
            nodes+=nd
    return nodes
def dfs(adj,v): # a schema of bfs
    visited=[False]*(v+1)
    li=[]
    for i in range(v):
        if visited[i]==False:
            nodes=dfshelper(adj,i,visited)
            li.append(nodes)

    return li
#####################################################################################
mx=10**9+7
def solve():
    n=II()
    li=L()
    li.sort()
    d={}
    for i in range(n-1):
        ele=li[i+1]-li[i]
        d[ele]=d.get(ele,0)+1
    if len(d)>2:
        print(0)
    elif len(d)==0:
        print(-1)
    else:
        if len(d)==1:
            x=list(d.keys())[0]
            if x==0:
                print(1)
                print(li[0])
            elif n==2 and x%2==0:
                print(3)
                print(li[0]-x,li[0]+x//2,li[-1]+x)
            else:
                print(2)
                print(li[0]-x,li[-1]+x)
        else:
            uni,com=-1,-1
            for ele in d:
                if d[ele]==1 and uni==-1:
                    uni=ele
                else:
                    com=ele
            if n==3:
                com,uni=min(uni,com),max(uni,com)
                if uni!=2*com:
                    print(0)
                else:
                    print(1)
                    for i in range(n-1):
                        if li[i+1]-li[i]==uni:
                            print(li[i]+com)
            else:
                if uni<com or uni!=2*com:
                    print(0)
                else:
                    print(1)
                    for i in range(n-1):
                        if li[i+1]-li[i]==uni:
                            print(li[i]+com)


solve()

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