You are given an array a consisting of n non-negative integers.

You have to replace each 0 in a with an integer from 1 to n (different elements equal to 0 can be replaced by different integers).

The value of the array you obtain is the number of integers k from 1 to n such that the following condition holds: there exist a pair of adjacent elements equal to k (i. e. there exists some i ∈ [1, n - 1] such that a_i = a_{i + 1} = k). If there are multiple such pairs for some integer k, this integer is counted in the value only once.

Your task is to obtain the array with the maximum possible value.

Input

The first line contains one integer n (2 ≤ n ≤ 3 ⋅ 10^5) — the number of elements in the array.

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ min(n, 600)) — the elements of the array.

Output

Print n integers not less than 1 and not greater than n — the array with the maximum possible value you can obtain.

If there are multiple answers, print any of them.

Examples

Input


4
1 1 0 2


Output


1 1 2 2 


Input


5
0 0 0 0 0


Output


3 1 1 3 3


Input


5
1 2 3 4 5


Output


1 2 3 4 5 


Input


6
1 0 0 0 0 1


Output


1 2 3 3 1 1


Input


3
3 0 2


Output


3 2 2 


Input


5
1 0 2 0 1


Output


1 2 2 1 1 


Input


7
1 0 2 3 1 0 2


Output


1 2 2 3 1 1 2

Source: codeforces | Difficulty: VERY_HARD
Tags: Flows and cuts

Constructive algorithms


Solutions: