Dadas and Damyoo, before hosting the Lemon Cup, are arguing over the arrangement of the problems. Dadas has arranged the $N$ problems in increasing order of difficulty like the following figure.

Note that the difficulties shown in the picture have no relation to the actual difficulties of the problems. However, Damyoo does not like this arrangement and wants to arrange the problems in decreasing order of difficulty.

Damyoo can use the following operation to reverse the order of the problems.

$$s_1 \ e_1 \ s_2 \ e_2$$

This is an operation that reverses the order from the $s_1$-th problem to the $e_1$-th problem, and from the $s_2$-th problem to the $e_2$-th problem, respectively.

The following conditions must be satisfied.

• $e_1 - s_1 = e_2 - s_2$.
• $1 \leq s_1 \lt e_1 \lt s_2 \lt e_2 \leq N$.

Determine whether it is possible to completely reverse the order of the problems using the given operation, and if possible, print the process.

The input is given in the following format.

$N$

If the order of the problems cannot be completely reversed, print -1 on the first line.

Otherwise, print the number of operations $Q$ performed by Damyoo on the first line.

From the second line, print four integers $s_1, e_1, s_2, e_2$ separated by a space representing the $i$-th operation on the $(i+1)$-th line over $Q$ lines.

• $8 \leq N \leq 100\ 000$.