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.
from __future__ import division, print_function
import bisect
import math
import itertools
import sys
import heapq
from atexit import register
 
if sys.version_info[0] < 3:
    from io import BytesIO as stream
else:
    from io import StringIO as stream
 
 
if sys.version_info[0] < 3:
    class dict(dict):
        """dict() -> new empty dictionary"""
        def items(self):
            """D.items() -> a set-like object providing a view on D's items"""
            return dict.iteritems(self)
 
        def keys(self):
            """D.keys() -> a set-like object providing a view on D's keys"""
            return dict.iterkeys(self)
 
        def values(self):
            """D.values() -> an object providing a view on D's values"""
            return dict.itervalues(self)
 
    input = raw_input
    range = xrange
 
    filter = itertools.ifilter
    map = itertools.imap
    zip = itertools.izip
 
 
def sync_with_stdio(sync=True):
    """Set whether the standard Python streams are allowed to buffer their I/O.
 
    Args:
        sync (bool, optional): The new synchronization setting.
 
    """
    global input, flush
 
    if sync:
        flush = sys.stdout.flush
    else:
        sys.stdin = stream(sys.stdin.read())
        input = lambda: sys.stdin.readline().rstrip('\r\n')
 
        sys.stdout = stream()
        register(lambda: sys.__stdout__.write(sys.stdout.getvalue()))
 
def main():
    
    
    
    n=int(input()) 
    ans=[]
    #n,k=map(int, input().split())
    a=list(map(int, input().split()))
    b=[0]*(n+1)
    #if a[0]==0: ans.append(1)
    #if a[0]: ans.append(0)
    for i in range(n):
        b[a[i]]=1
        if a[i]>(i+1):
            print('-1')
            exit()
    hp=[]
    for i in range(n+1):
        if not b[i]: hp.append(i)
    heapq.heapify(hp)
    #x=heapq.heappop(hp)
    for i in range(n-1):
        ans.append(heapq.heappop(hp))
        if a[i]<a[i+1]:
            heapq.heappush(hp,a[i])
    ans.append(heapq.heappop(hp))        
    #print(ans,list(hp))    
    c=[0]*(n+1)
    mi=0
    for i in range(n):
        c[ans[i]]=1
        while(c[mi]==1):
            mi+=1
        if mi != a[i]:
            print('-1')
            exit()
    print(*ans)        
    
if __name__ == '__main__':
    sync_with_stdio(False)
    main()