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()))
k = 0
b = [0]*n
s = set(a)
t = [False for i in range(n)]
for i in range(1,n):
	if a[i] != a[i-1]:
		b[i] = a[i-1]
		t[i] = True
if a[0] == 0:
	b[0] = 1
else:
	b[0] = a[0] - 1
m = b[0]
for i in range(1,n):
	if not t[i]:
		m+=1
		while True:
			if m not in s:
				b[i] = m
				break
			else:
				m+=1
for i in b:print(i,end = " ")