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A. Co-prime Array

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given an array of *n* elements, you must make it a co-prime array in as few moves as possible.

In each move you can insert any positive integral number you want not greater than 10^{9} in any place in the array.

An array is co-prime if any two adjacent numbers of it are co-prime.

In the number theory, two integers *a* and *b* are said to be co-prime if the only positive integer that divides both of them is 1.

Input

The first line contains integer *n* (1 ≤ *n* ≤ 1000) — the number of elements in the given array.

The second line contains *n* integers *a*_{i} (1 ≤ *a*_{i} ≤ 10^{9}) — the elements of the array *a*.

Output

Print integer *k* on the first line — the least number of elements needed to add to the array *a* to make it co-prime.

The second line should contain *n* + *k* integers *a*_{j} — the elements of the array *a* after adding *k* elements to it. Note that the new array should be co-prime, so any two adjacent values should be co-prime. Also the new array should be got from the original array *a* by adding *k* elements to it.

If there are multiple answers you can print any one of them.

Example

Input

3

2 7 28

Output

1

2 7 9 28

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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