CF1869A.Make It Zero

During Zhongkao examination, Reycloer met an interesting problem, but he cannot come up with a solution immediately. Time is running out! Please help him.

Initially, you are given an array $a$ consisting of $n \ge 2$ integers, and you want to change all elements in it to $0$ .

In one operation, you select two indices $l$ and $r$ ( $1\le l\le r\le n$ ) and do the following:

• Let $s=a_l\oplus a_{l+1}\oplus \ldots \oplus a_r$ , where $\oplus$ denotes the bitwise XOR operation;
• Then, for all $l\le i\le r$ , replace $a_i$ with $s$ .

You can use the operation above in any order at most $8$ times in total.

Find a sequence of operations, such that after performing the operations in order, all elements in $a$ are equal to $0$ . It can be proven that the solution always exists.

The first line of input contains a single integer $t$ ( $1\le t\le 500$ ) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $n$ ( $2\le n\le 100$ ) — the length of the array $a$ .

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ( $0\le a_i\le 100$ ) — the elements of the array $a$ .

For each test case, in the first line output a single integer $k$ ( $0\le k\le 8$ ) — the number of operations you use.

Then print $k$ lines, in the $i$ -th line output two integers $l_i$ and $r_i$ ( $1\le l_i\le r_i\le n$ ) representing that you select $l_i$ and $r_i$ in the $i$ -th operation.

Note that you do not have to minimize $k$ . If there are multiple solutions, you may output any of them.

In the first test case, since $1\oplus2\oplus3\oplus0=0$ , after performing the operation on segment $[1,4]$ , all the elements in the array are equal to $0$ .

In the second test case, after the first operation, the array becomes equal to $[3,1,4,15,15,15,15,6]$ , after the second operation, the array becomes equal to $[0,0,0,0,0,0,0,0]$ .

In the third test case:

Operation $a$ before $a$ after $1$ $[\underline{1,5},4,1,4,7]$ $\rightarrow$ $[4,4,4,1,4,7]$ $2$ $[4,4,\underline{4,1},4,7]$ $\rightarrow$ $[4,4,5,5,4,7]$ $3$ $[4,4,5,5,\underline{4,7}]$ $\rightarrow$ $[4,4,5,5,3,3]$ $4$ $[\underline{4,4,5},5,3,3]$ $\rightarrow$ $[5,5,5,5,3,3]$ $5$ $[5,5,5,\underline{5,3,3}]$ $\rightarrow$ $[5,5,5,5,5,5]$ $6$ $[\underline{5,5,5,5,5,5}]$ $\rightarrow$ $[0,0,0,0,0,0]$ In the fourth test case, the initial array contains only $0$ , so we do not need to perform any operations with it.