Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Journey

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe territory of Berland is represented by a rectangular field *n* × *m* in size. The king of Berland lives in the capital, located on the upper left square (1, 1). The lower right square has coordinates (*n*, *m*). One day the king decided to travel through the whole country and return back to the capital, having visited every square (except the capital) exactly one time. The king must visit the capital exactly two times, at the very beginning and at the very end of his journey. The king can only move to the side-neighboring squares. However, the royal advise said that the King possibly will not be able to do it. But there is a way out — one can build the system of one way teleporters between some squares so that the king could fulfill his plan. No more than one teleporter can be installed on one square, every teleporter can be used any number of times, however every time it is used, it transports to the same given for any single teleporter square. When the king reaches a square with an installed teleporter he chooses himself whether he is or is not going to use the teleport. What minimum number of teleporters should be installed for the king to complete the journey? You should also compose the journey path route for the king.

Input

The first line contains two space-separated integers *n* and *m* (1 ≤ *n*, *m* ≤ 100, 2 ≤ *n* · *m*) — the field size. The upper left square has coordinates (1, 1), and the lower right square has coordinates of (*n*, *m*).

Output

On the first line output integer *k* — the minimum number of teleporters. Then output *k* lines each containing 4 integers *x*_{1} *y*_{1} *x*_{2} *y*_{2} (1 ≤ *x*_{1}, *x*_{2} ≤ *n*, 1 ≤ *y*_{1}, *y*_{2} ≤ *m*) — the coordinates of the square where the teleporter is installed (*x*_{1}, *y*_{1}), and the coordinates of the square where the teleporter leads (*x*_{2}, *y*_{2}).

Then print *nm* + 1 lines containing 2 numbers each — the coordinates of the squares in the order in which they are visited by the king. The travel path must start and end at (1, 1). The king can move to side-neighboring squares and to the squares where a teleporter leads. Besides, he also should visit the capital exactly two times and he should visit other squares exactly one time.

Examples

Input

2 2

Output

0

1 1

1 2

2 2

2 1

1 1

Input

3 3

Output

1

3 3 1 1

1 1

1 2

1 3

2 3

2 2

2 1

3 1

3 2

3 3

1 1

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/19/2018 04:02:17 (d2).

Desktop version, switch to mobile version.

User lists

Name |
---|