Make It Zero
Description
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.
Input
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 $a$.
Output
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.
6
4
1 2 3 0
8
3 1 4 1 5 9 2 6
6
1 5 4 1 4 7
5
0 0 0 0 0
7
1 1 9 9 0 1 8
3
100 100 0
1
1 4
2
4 7
1 8
6
1 2
3 4
5 6
1 3
4 6
1 6
0
4
1 2
6 7
3 4
6 7
1
1 2
Note
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.