There is an $m \times n$ grid, with coordinates starting from 0. Initially, every cell is filled with $-1$.

An operation consists of selecting a "Z-shape" region (as shown in the image, which can be rotated and flipped) and changing the sign of the numbers in those cells.

Given $m$ and $n$, determine if there exists a sequence of operations that changes all numbers in the grid to $1$.

If no such sequence of operations exists, output Impossible!.

Z-shape and its rotations/flips

Input

The input contains two integers $m, n$ ($2 \le m, n \le 2 \times 10^5$, $4 \le mn \le 2 \times 10^5$), representing the number of rows and columns of the grid.

Output

If a solution exists, output the sequence of operations: the first line should contain the number of operations $r$ ($0 \le r \le 10^6$), followed by $r$ lines, each containing 8 integers representing the coordinates of the four cells of the "Z-shape" (in the order $x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_4$, where the order of the four points is arbitrary). If no solution exists, output Impossible!. If there are multiple solutions, any one is acceptable.

It can be proven that if a valid solution exists, there must exist a valid solution such that $0 \le r \le 10^6$.

Examples

Input 1

2 4

Output 1

4
0 0 0 1 1 1 1 2
1 0 1 1 0 1 0 2
1 3 0 1 1 2 0 2
1 1 1 2 0 2 0 3

Input 2

2 5

Output 2

Impossible!