Powerful Ksenia
Description
Ksenia has an array $a$ consisting of $n$ positive integers $a_1, a_2, \ldots, a_n$.
In one operation she can do the following:
- choose three distinct indices $i$, $j$, $k$, and then
- change all of $a_i, a_j, a_k$ to $a_i \oplus a_j \oplus a_k$ simultaneously, where $\oplus$ denotes the bitwise XOR operation.
She wants to make all $a_i$ equal in at most $n$ operations, or to determine that it is impossible to do so. She wouldn't ask for your help, but please, help her!
The first line contains one integer $n$ ($3 \leq n \leq 10^5$) — the length of $a$.
The second line contains $n$ integers, $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 10^9$) — elements of $a$.
Print YES or NO in the first line depending on whether it is possible to make all elements equal in at most $n$ operations.
If it is possible, print an integer $m$ ($0 \leq m \leq n$), which denotes the number of operations you do.
In each of the next $m$ lines, print three distinct integers $i, j, k$, representing one operation.
If there are many such operation sequences possible, print any. Note that you do not have to minimize the number of operations.
Input
The first line contains one integer $n$ ($3 \leq n \leq 10^5$) — the length of $a$.
The second line contains $n$ integers, $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 10^9$) — elements of $a$.
Output
Print YES or NO in the first line depending on whether it is possible to make all elements equal in at most $n$ operations.
If it is possible, print an integer $m$ ($0 \leq m \leq n$), which denotes the number of operations you do.
In each of the next $m$ lines, print three distinct integers $i, j, k$, representing one operation.
If there are many such operation sequences possible, print any. Note that you do not have to minimize the number of operations.
Samples
5
4 2 1 7 2
YES
1
1 3 4
4
10 4 49 22
NO
Note
In the first example, the array becomes $[4 \oplus 1 \oplus 7, 2, 4 \oplus 1 \oplus 7, 4 \oplus 1 \oplus 7, 2] = [2, 2, 2, 2, 2]$.