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.
n = int(input())
a=list(map(int,input().split()))
 
f=1
for i in range(n):
    if  a[i]>i+1:
        f=0
        break
if f==0:
    print(-1)
else:
    ans = [-1]*(n+1)
    ind = [-1]*(n+1)
    for i in range(n):
        ind[a[i]]=i
    done=[0]*(n+1)
    for i in range(len(ind)):
        if ind[i]!=-1:
            ans[ind[i]+1]=i
            done[i]=1
    i=0
    j=0
    while(i<n):
        if ans[i]==-1:
            while(j<n+1):
                if done[j]==0:
                    ans[i]=j
                    done[j]=1
                    break
                else:j+=1
        i+=1
    print(*ans[0:n])
                    
            
    
    
    

    
                
    
    
        