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
input=sys.stdin.readline
t=1
for _ in range(t):
    maxi=10**6
    n=int(input())
    arr=list(map(int,input().split()))
    l=[-1]*n
    vacant=n
    left=max(arr)
    cur=arr[0]
    used=[-1]*(10**6+1)
    allow=arr[-1]-1


    for i in range(n):
        if(arr[i]!=cur):
            l[i]=cur
            used[cur]=1
            cur=arr[i]
            vacant-=1
            
            left-=1
    if(l[-1]==-1):        
        l[-1]=10**6
        used[10**6]=1
        vacant-=1
    
    for i in range(n-2,-1,-1):
        while(used[allow]==1):
            allow-=1
        while(used[maxi]==1):
            maxi-=1
        #print(i,allow)
        if((arr[i]<allow or vacant<=left) and allow>=0):
            if(l[i]==-1):
                l[i]=allow
                
                used[allow]=1
                allow-=1
                left-=1
                vacant-=1
        elif(arr[i]>=allow):
            if(l[i]==-1):
                l[i]=maxi
                
                used[maxi]=1
                maxi-=1
                vacant-=1
    #print(used[1])   
    #print(left)
    if(arr[0]==1 and len(arr)==1):
        print(0)
    elif(left>0):
        print(-1)
        #print(*l)
    else:
        print(*l)
        
    
        
    