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()))
b=[]
c=[]
d=dict()
for j in range(n):
    if a[j]  in d.keys():
        d[a[j]]+=1
    else:
        d[a[j]]=1
        c.append(a[j])
j=0
i=2
while(j<len(c)):
    p=c[j]
    k=d[c[j]]-1
    if j==0:
        if a[j]==0:
            b.append(1)
        else:
            b.append(0)
    else:
        b.append(c[j-1])
    p=0
    while(p<k):
        if i in d.keys():
            pass
        else:
            b.append(i)
            p+=1
        i+=1
    j+=1
else:
    print(*b)






