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=input()
a=map(int,raw_input().split())
b=[10**6 for i in range(n)]
req=[0 for i in range(n+1)]
c=1
modi=[]
ans=[str(10**6) for j in range(n)]
for  i in range(n):
    if a[i]>(i+1):
        print -1;c=0;
        break
    modi.append(i)
    if i:
        if a[i]!=a[i-1]:
            p=i
            for j in range(a[i-1],a[i]):
                if len(modi)==0:
                    c=0;print -1;break
                k=modi.pop()
                ans[k]=str(j)
                
        
                
        
    else:
        if a[i]==1:
            ans[0]="0"
        
if c:
    s=" "
    print s.join(ans)
        