Triple Flips

Description:

Input:

The first line contains a single integer $$$n$$$ ($$$3 \le n \le 10^5$$$) — the length of the array.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 1$$$) — the elements of the array.

Output:

Print "YES" (without quotes) if the answer exists, otherwise print "NO" (without quotes). You can print each letter in any case (upper or lower).

If there is an answer, in the second line print an integer $$$m$$$ ($$$0 \le m \le (\lfloor \frac{n}{3} \rfloor + 12)$$$) — the number of operations in your answer.

After that in ($$$i + 2$$$)-th line print the $$$i$$$-th operations — the integers $$$x_i, y_i, z_i$$$. You can print them in arbitrary order.

Sample Input:

5
1 1 0 1 1

Sample Output:

YES
2
1 3 5
2 3 4

Sample Input:

3
0 1 0

Sample Output:

NO

Note:

In the first sample the shown output corresponds to the following solution:

• 1 1 0 1 1 (initial state);
• 0 1 1 1 0 (the flipped positions are the first, the third and the fifth elements);
• 0 0 0 0 0 (the flipped positions are the second, the third and the fourth elements).

Other answers are also possible. In this test the number of operations should not exceed $$$\lfloor \frac{5}{3} \rfloor + 12 = 1 + 12 = 13$$$.

In the second sample the only available operation is to flip all the elements. This way it is only possible to obtain the arrays 0 1 0 and 1 0 1, but it is impossible to make all elements equal to zero.