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ZOJ Problem Set - 3846
GCD Reduce

Time Limit: 2 Seconds      Memory Limit: 65536 KB      Special Judge

You are given a sequence {A1, A2, ..., AN}. You task is to change all the element of the sequence to 1 with the following operations (you may need to apply it multiple times):

  • choose two indexes i and j (1 ≤ i < jN);
  • change both Ai and Aj to gcd(Ai, Aj), where gcd(Ai, Aj) is the greatest common divisor of Ai and Aj.

You do not need to minimize the number of used operations. However, you need to make sure that there are at most 5N operations.


Input will consist of multiple test cases.

The first line of each case contains one integer N (1 ≤ N ≤ 105), indicating the length of the sequence. The second line contains N integers, A1, A2, ..., AN (1 ≤ Ai ≤ 109).


For each test case, print a line containing the test case number (beginning with 1) followed by one integer M, indicating the number of operations needed. You must assure that M is no larger than 5N. If you cannot find a solution, make M equal to -1 and ignore the following output.

In the next M lines, each contains two integers i and j (1 ≤ i < jN), indicating an operation, separated by one space.

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

Remember to print a blank line after each case. But extra spaces and blank lines are not allowed.

Sample Input

2 2 3 4
2 2 2 2

Sample Output

Case 1: 3
1 3
1 2
1 4

Case 2: -1

Author: LIN, Xi
Source: ZOJ Monthly, January 2015
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