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.
def g(a):
 last=-1
 for ai in a:
  for j in xrange(last+1,ai): yield j
  last=ai
 while True: last+=1; yield last

def f(n,a):
 for i in xrange(n):
  if a[i]>i+1: return False
 a.insert(0,0)
 t=g(a); out=[]
 for i in xrange(1,len(a)):
  if a[i]==a[i-1]: out.append(t.next())
  else: out.append(a[i-1])
 return out

n=int(raw_input())
a=map(int,raw_input().split())
u=f(n,a)
print (' '.join(map(str,u)) if u else -1)
