Little Petya loves playing with rectangles. Mom bought Petya a rectangle divided into cells n × m in size (containing n rows, m columns). Petya marked two different cells of the rectangle and now he is solving the following task:

Let's define a simple path between those two cells as a sequence of distinct cells a₁, a₂, ..., a_k, where a₁ and a_k are the two marked cells. Besides, a_i and a_i + 1 are side-neighboring cells of the path (1 ≤ i < k). Let's denote the path length as number k (the sequence length).

Petya's task is to find the longest simple path's length and to print the path. Help him.

Input

The first line contains space-separated integers n and m (4 ≤ n, m ≤ 1000) — the number of rows and the number of columns in the rectangle, correspondingly. The second line contains space-separated integers x₁ and y₁ — the coordinates of the first marked cell. The third line contains space-separated integers x₂ y₂ — the coordinates of the second marked cell (1 < x₁, x₂ < n, 1 < y₁, y₂ < m, x₁ ≠ x₂, y₁ ≠ y₂).

The coordinates of a marked cell are a pair of integers x y, where x represents the row's number and y represents the column's number. The rows are numbered from top to bottom with consecutive integers from 1 to n. The columns are numbered from the left to the right by consecutive integers from 1 to m.

It is guaranteed that the marked cells are not positioned in one row or column.

Output

In the first line print the length of the found path — k. In the next lines print k pairs of integers, one per line — coordinates of the cells that constitute the found path in the order, in which they follow in the path (the path must go from cell (x₁, y₁) to cell (x₂, y₂)). If there are several solutions, print any of them.

Note

The statement test is described in the picture:

$\text{[math]}$

Idx	Name	Rating
A	Petya and Inequiations	1400
B	Petya and Divisors	1900
C	Petya and Spiders	2100
D	Petya and Coloring	2300
E	Petya and Rectangle	2900

Codeforces Beta Round 85 (Div. 1 Only)