Make It Zero
题面翻译
给定一个长度为 $n$ 的数列 $a$，定义一次操作为：
- 选择两个数 $l,r$，且 $1 \le l \le r \le n$。
- 记 $x= a_l \oplus a_{l+1} \oplus … \oplus a_{r-1} \oplus a_r$。
- 将 $a_i$ 替换为 $x$，其中 $i \in [l,r]$。
目的是把 $a$ 的所有元素变成 $0$ 且不超过 $8$ 次操作，请你输出一种方案，第一行为操作次数，记作 $k$，接下来 $k$ 行每行两个数表示选择的 $l,r$。
多测，$1 \le t \le 500, 2 \le n \le 100, 0 \le a_i \le 100$。
题目描述
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.
输入格式
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 $ .
输出格式
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.
样例 #1
样例输入 #1
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
样例输出 #1
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
提示
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.
