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())
lis = list(map(int,input().split()))
maxi = lis[-1]
k = n - 1
flag = 1
ans = []
if maxi > n:
    flag = -1
if flag == -1:
    print(-1)
else:
    xtra = 0
    points = []
    if lis[0] == 0:
        ans.append(maxi+1)
        xtra = xtra + 1
        points.append(0)
    elif lis[0] == 1:
        ans.append(0)
    else:
        flag = -1
    if flag != -1:    
        for i in range(1,n):
            l = lis[i]
            if l == lis[i-1]:
                ans.append(maxi+1)
                xtra = xtra + 1
                points.append(i)
            else:
                if lis[i] == lis[i-1] + 1:
                    ans.append(lis[i-1])
                else:
                    dif = lis[i] - lis[i-1] - 1
                    if dif > xtra:
                        flag = -1
                        break
                    else:
                        for j in range(lis[i-1] + 1,lis[i]):
                            ans[points[0]] = j
                            points.pop(0)
                            xtra = xtra - 1
                        ans.append(lis[i-1])
    if flag == -1:
        print(-1)
    else:
        print(*ans,sep= " ")