1364_C. Ehab and Prefix MEXs
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.
```python
n=int(input())
arr=list(map(int,input().split()))
flag=0
vis=[0]*(10**6+1)
for i in range(n):
    if arr[i]>i+1:
        flag=1
    vis[arr[i]]=1
if flag==1:
    print(-1)
    quit()
b=[-1]*(n)
for i in range(1,n):
    if arr[i-1]!=arr[i]:
        b[i]=arr[i-1]
not_vis=[]
for i in range(10**6+1):
    if vis[i]==0:
        not_vis.append(i)
j=0
for i in range(n):
    if b[i]==-1:
        b[i]=not_vis[j]
        j+=1
print(*b)


```