CF660A.Co-prime Array

You 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 109 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.

给你一个包含 $n$ 个元素的数组，你需要以最少的操作次数将其变为一个互质数组。

在每次操作中，你可以在数组的任意位置插入一个不超过 $10^9$ 的任意正整数。

若一个数组中任意两个相邻元素均互质，则该数组称为互质数组。

在数论中，若两个整数 $a$ 和 $b$ 的唯一正公因数为 $1$，则称它们互质。

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 ≤ 109) — the elements of the array a.

第一行包含一个整数 $n$（$1 \leq n \leq 1000$）—— 给定数组中的元素个数。

第二行包含 $n$ 个整数 $a_i$（$1 \leq a_i \leq 10^9$）—— 数组 $a$ 的元素。

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.

第一行输出整数 $k$ —— 使数组 $a$ 变为互质数组所需添加的最少元素个数。

第二行输出 $n + k$ 个整数 $a_j$ —— 在向原数组 $a$ 添加 $k$ 个元素后所得的新数组。注意，新数组必须是互质的，即任意两个相邻元素必须互质；同时，该新数组必须由原数组 $a$ 通过添加 $k$ 个元素得到。

若存在多个合法答案，输出任意一个即可。