D. Powerful Kseniatime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputKsenia 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!InputThe 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.OutputPrint 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.ExamplesInput
5
4 2 1 7 2
Output
YES
1
1 3 4Input
4
10 4 49 22
Output
NO
NoteIn 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].
5
4 2 1 7 2

YES 1 1 3 4
['bitmasks', 'constructive algorithms', 'math', '*2200']