Codeforces Global Round 18 |
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Finished |

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constructive algorithms

graph matchings

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G. Maximum Adjacent Pairs

time limit per test

3 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputYou 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 $$$i \in [1, n - 1]$$$ 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 $$$n$$$ ($$$2 \le n \le 3 \cdot 10^5$$$) — the number of elements in the array.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le \min(n, 600)$$$) — 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

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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