Problem:
Score : 400 points

Problem Statement

There is a grid of square cells with H horizontal rows and W vertical columns. The cell at the i-th row and the j-th column will be denoted as Cell (i, j).

In Cell (i, j), a_{ij} coins are placed.

You can perform the following operation any number of times:

Operation: Choose a cell that was not chosen before and contains one or more coins, then move one of those coins to a vertically or horizontally adjacent cell.

Maximize the number of cells containing an even number of coins.

Constraints

All values in input are integers.

1 \leq H, W \leq 500

0 \leq a_{ij} \leq 9

Input

Input is given from Standard Input in the following format:

H W
a_{11} a_{12} ... a_{1W}
a_{21} a_{22} ... a_{2W}
:
a_{H1} a_{H2} ... a_{HW}

Output

Print a sequence of operations that maximizes the number of cells containing an even number of coins, in the following format:

N
y_1 x_1 y_1' x_1'
y_2 x_2 y_2' x_2'
:
y_N x_N y_N' x_N'

That is, in the first line, print an integer N between 0 and H \times W (inclusive), representing the number of operations.

In the (i+1)-th line (1 \leq i \leq N), print four integers y_i, x_i, y_i' and x_i' (1 \leq y_i, y_i' \leq H and 1 \leq x_i, x_i' \leq W), representing the i-th operation. These four integers represents the operation of moving one of the coins placed in Cell (y_i, x_i) to a vertically or horizontally adjacent cell, (y_i', x_i').

Note that if the specified operation violates the specification in the problem statement or the output format is invalid, it will result in Wrong Answer.

Sample Input 1

2 3
1 2 3
0 1 1

Sample Output 1

3
2 2 2 3
1 1 1 2
1 3 1 2

Every cell contains an even number of coins after the following sequence of operations:

Move the coin in Cell (2, 2) to Cell (2, 3).

Move the coin in Cell (1, 1) to Cell (1, 2).

Move one of the coins in Cell (1, 3) to Cell (1, 2).

Sample Input 2

3 2
1 0
2 1
1 0

Sample Output 2

3
1 1 1 2
1 2 2 2
3 1 3 2

Sample Input 3

1 5
9 9 9 9 9

Sample Output 3

2
1 1 1 2
1 3 1 4

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

# なぜか 4WA
# ってか最初のテストケースでREなるのなんなん

# Dは不変なのでaiからai+1には必ずたどり着け、
# 最短でai+1 - aiぶん一気にすすむ1手、
# 最長で1ずつすすむ ai+1 - ai 手
# それぞれの差をとって1~最大公約数の約数を試していき、
# スタート地点から最も近い場所に到達できればその値ですべての都市を回れる
# （行き過ぎたら 次の値を試す）


# という方針でやったら2WAだったのだがどこが間違ってるのかわからん

# 諦めて解説をみたら全部の位置とのgcdを取るという感じで納得感が薄い

# difのとこがおかしかった（n=2の場合）のを直してみたバージョン
# ↑やっただけでTLEになったのでマジで鬱になった ふつうに解答通り終わらせるためだけの自戒バージョン

n, pos = gets.chomp.split.map(&:to_i)
@cities = gets.chomp.split.map(&:to_i).sort
# 最初にn==1の場合だけやっとく 1ずつしか進めない
if n==1
  puts (@cities[0]-pos).abs
  exit
end
<<~EOS
dif = []  # 各都市間の差
(n-1).times do |i|
  dif << @cities[i+1] - @cities[i]
end
EOS

def gcd(a, b)
  return a if b.zero?
  return gcd(b, a) if a<b
  return gcd(b, a%b)
end

gcdn = gcd((pos - @cities[0]).abs, (pos - @cities[1]).abs)
(n-2).times do |i|
  gcdn = gcd(gcdn, (pos-@cities[i+2]).abs)
end
puts gcdn
<<~EOS
# 各都市間の差の最大公約数
gcdn = 1
if dif.size == 1
  # これを忘れていたっぽい
  gcdn = gcd(dif[0], pos)
end
if dif.size >= 2
  gcdn = gcd(dif[0], dif[1])
end
2.upto(n-2) do |i|
  gcdn = gcd(dif[i], gcdn)  # これが間違ってたっぽい
end
# 約数をとる ダルいのでgcdn/2までループすればいいんじゃないかな
yakusu = []
1.upto(gcdn/2) do |i|
  if (gcdn % i).zero?
    yakusu << i
  end
end
yakusu << gcdn
yakusu.reverse!
# これのでかいやつから試していって到達できればおｋ
# 最も速く到達できるやつをにぶたんで求める（どうせ到達できるので「posを越える最小の値」を求める）
# そもそもposが既に配列にある場合もあるか
if @cities[-1] < pos
  goal = @cities[-1]
  # 実装するの忘れてた 1WA
  yakusu.each do |y|
    if (pos-goal)%y == 0
      puts y
      exit
    end
  end
elsif @cities[-1] == pos
  # 2番目に大きいやつに向けて下っていく
  goal = @cities[-2]
  # 実装するの忘れてた 1WA
  yakusu.each do |y|
    if (pos-goal)%y == 0
      puts y
      exit
    end
  end
else
  # にぶたんで求める
  l, r = 0, n
  while r-l>1 do
    mid = (r+l)/2
    if @cities[mid] < pos
      l = mid + 1
    else
      r = mid
    end
  end
  # lが求めるやつね
  goal = @cities[l]
  if goal == pos
    goal = @cities[l+1]
  end
  yakusu.each do |y| 
    if (goal-pos)%y == 0
      puts y
      exit
    end
  end
end
EOS