Given an array a of length n, find another array, b, of length n such that:

  * for each i (1 ≤ i ≤ n) MEX(\\{b_1, b_2, …, b_i\})=a_i. 



The MEX of a set of integers is the smallest non-negative integer that doesn't belong to this set.

If such array doesn't exist, determine this.

Input

The first line contains an integer n (1 ≤ n ≤ 10^5) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ i) — the elements of the array a. It's guaranteed that a_i ≤ a_{i+1} for 1≤ i < n.

Output

If there's no such array, print a single line containing -1.

Otherwise, print a single line containing n integers b_1, b_2, …, b_n (0 ≤ b_i ≤ 10^6)

If there are multiple answers, print any.

Examples

Input


3
1 2 3


Output


0 1 2 

Input


4
0 0 0 2


Output


1 3 4 0 

Input


3
1 1 3


Output


0 2 1 

Note

In the second test case, other answers like [1,1,1,0], for example, are valid.
import sys
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__


n=int(input())
arry = list(map(int,input().split()))



ans=[]

##arrangepoint=[]
##for i in range(n):
##
##    if arry[i]==i+1:
##        arrangepoint.append(i)
dic={}
toreach='notyet'
for i in range(n):
    curr=arry[n-1-i]

    gotans=False

    if toreach=='notyet':
        toreach=curr-1
    if i<n-1:
        prevele=arry[n-2-i]
        if prevele<curr:
            gotans=True
            ans=[prevele]+ans
            dic[prevele]=True
        elif prevele==curr and n-i-1==prevele:
            ans=[n]+ans
            gotans=True
    if not gotans:
        foundpoint='no'
        while True:
            if toreach<0:
                break
            else:
                ina=dic.get(toreach,False)
                if not ina:
                    foundpoint=toreach
                    dic[foundpoint]=True
                    break
            toreach-=1
        if foundpoint=='no':
            ans=[n]+ans
        else:
            ans=[foundpoint]+ans

if arry[0]==1:
    ans[0]=0
elif arry[0]==0:
    ans[0]=1

print(" ".join(str(x) for x in ans))

