D. Powerful Ksenia
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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!

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.

Examples
Input
5
4 2 1 7 2

Output
YES
1
1 3 4
Input
4
10 4 49 22

Output
NO

Note

In the first example, the array becomes $[4 \oplus 1 \oplus 7, 2, 4 \oplus 1 \oplus 7, 4 \oplus 1 \oplus 7, 2] = [2, 2, 2, 2, 2]$.