Tri XOR Codechef Solution

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Tri XOR Codechef Solution

Tri XOR Codechef Solution

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Problem

There are N numbers written on a blackboard.

In one operation, Chef can:

  • Choose any 3 integers A, B, and C written on the blackboard.
  • Erase them from the blackboard.
  • Write A \oplus B, B \oplus C, and C \oplus A on the blackboard. Here, \oplus denotes the bitwise XOR operation.

Your task is to make all the numbers written on the blackboard equal to 0 using at most 11111 operations.

It is guaranteed that all the numbers on the blackboard can be made 0 under the given constraints.

Input Format

  • The first line of input will contain a single integer T, denoting the number of test cases.
  • Each test case consists of multiple lines of input.
    • The first line of each test case contains a single integer N, the number of integers written on the blackboard.
    • Next line contains N space separated integers A_1, A_2, \dots A_N, the integers written on the blackboard initially.

Output Format

For each test case:

  • On the first line, output M (0 \leq M \leq 11111) – the number of operations you are going to perform.
  • Next M lines contain 3 space-separated integers A, B, and C (A, B, C should be present on the blackboard at the time of operation ) – denoting the integers using which operation is performed.

Constraints

  • 1 \leq T \leq 10
  • 6 \leq N \leq 1000
  • 0 \leq A_i \leq 10^9

Sample 1:

Input

Output

1
6
0 1 2 3 2 0
2
2 3 2
1 1 1

Explanation:

Test case 1: We can make all the numbers 0 using 2 operations:

  • Operation 1: Choose the integers 2, 3, and 2 and replace them with 2\oplus 3 = 1, 3\oplus 2 = 1, and 2\oplus 2 = 0. Thus, numbers on the blackboard are now [0, 1, 0, 1, 1, 0].
  • Operation 2: Choose the integers 1, 1, and 1 and replace them with 1\oplus 1 = 0, 1\oplus 1 = 0, and 1\oplus 1 = 0. Thus all numbers on the blackboard are now 0.
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SOLUTION

Tri XOR Codechef Solution

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