Prime Swaps

题意翻译

给出一个长度为 $n$ 的排列，每次你可以选择两个位置 $i, j~(i < j)$ ，并交换上面的数，前提是 $j - i + 1$ 是质数。 要求在 $5n$ 次操作内，把这个序列排号。输出具体排序的操作。

题目描述

You have an array $ a[1],a[2],...,a[n] $ , containing distinct integers from $ 1 $ to $ n $ . Your task is to sort this array in increasing order with the following operation (you may need to apply it multiple times): - choose two indexes, $ i $ and $ j $ ( $ 1<=i&lt;j<=n $ ; $ (j-i+1) $ is a prime number); - swap the elements on positions $ i $ and $ j $ ; in other words, you are allowed to apply the following sequence of assignments: $ tmp=a[i],a[i]=a[j],a[j]=tmp $ ( $ tmp $ is a temporary variable). You do not need to minimize the number of used operations. However, you need to make sure that there are at most $ 5n $ operations.

输入输出格式

输入格式

The first line contains integer $ n $ $ (1<=n<=10^{5}) $ . The next line contains $ n $ distinct integers $ a[1],a[2],...,a[n] $ $ (1<=a[i]<=n) $ .

输出格式

In the first line, print integer $ k $ $ (0<=k<=5n) $ — the number of used operations. Next, print the operations. Each operation must be printed as " $ i $ $ j $ " ( $ 1<=i&lt;j<=n $ ; $ (j-i+1) $ is a prime). If there are multiple answers, you can print any of them.

输入输出样例

输入样例 #1

3
3 2 1

输出样例 #1

1
1 3

输入样例 #2

2
1 2

输出样例 #2

0

输入样例 #3

4
4 2 3 1

输出样例 #3

3
2 4
1 2
2 4