Everybody knows that you are a _TensorFlow_ fan. Therefore, you've been challenged to recreate the _TensorFlow_ logo from two projections.
Consider that you have a _3D_ volume, $n times m times h$, and two projections (two matrices with dimensions $n times m$ and $n times h$ with elements $0$ and $1$). You are asked to compute a possible sets of cubes that must be placed inside the _3D_ volume such that the _3D_ object created with the cubes throws the shadows specified by the projection-matrices, when the light comes from left and front. If it is not possible, just print $-1$. If it is possible you must find exactly two sets, one with the *maximum* amount of cubes and one with the *minimum* amount. You can assume there is no gravitation (the cubes are located inside the _3D_ volume exactly where they are placed, without requiring any support). We assume that $1$ represents shadow and $0$ represents light.
If there are multiple such solutions, you must output the minimum lexicographic one. One solution $A$ is lexicographically smaller than another solution $b$ if the first number that differs between the two solutions is smaller in $a$ than in $b$.
For example, solution $[ (0, 0, 0), (1, 1, 1) ]$ is smaller than $[ (1, 1, 1), (0, 0, 0) ]$.
The first line contains three integers separated by a single space $n$, $m$, $h$ ($1 <= n, m, h <= 100$) — the volume dimensions.
Each of the next $n$ lines contains $m$ characters, each being either $1$ or $0$ representing either a shadow area ($1$) or a light area ($0$), describing the projection from the light in the front.
Each of the next $n$ lines contains $h$ characters, with the same format as above, describing the projection from the light on the left.
The output should contain on the first line one number, either $-1$ if there is no solution or $k_{m a x}$ representing the maximum number of cubes we can assign in the volume that will generate the two projections given in the input.
The next $k_{m a x}$ lines should contain triplets of numbers $x$, $y$, $z$ ($0 <= x < n$, $0 <= y < m$, $0 <= z < h$) representing the cubes chosen in the lexicographically smallest solution with maximum number of cubes.
Then, only if there is a solution, one more line follows containing $k_{m i n}$, the minimum number of cubes we can assign in the volume that will generate the two projections given in the input.
After that, the next $k_{m i n}$ lines should contain triplets of numbers $x$, $y$, $z$ ($0 <= x < n$, $0 <= y < m$, $0 <= z < h$) representing the cubes in the lexicographically smallest solution with minimum number of cubes.
A cube at coordinates $(x, y, z)$ will generate a shadow at line $x$ and column $y$ in the $n times m$ projection and line $x$ and column $z$ in the $n times h$ projection (indexed from $0$).
## Input
The first line contains three integers separated by a single space $n$, $m$, $h$ ($1 <= n, m, h <= 100$) — the volume dimensions. Each of the next $n$ lines contains $m$ characters, each being either $1$ or $0$ representing either a shadow area ($1$) or a light area ($0$), describing the projection from the light in the front.Each of the next $n$ lines contains $h$ characters, with the same format as above, describing the projection from the light on the left.
## Output
The output should contain on the first line one number, either $-1$ if there is no solution or $k_{m a x}$ representing the maximum number of cubes we can assign in the volume that will generate the two projections given in the input.The next $k_{m a x}$ lines should contain triplets of numbers $x$, $y$, $z$ ($0 <= x < n$, $0 <= y < m$, $0 <= z < h$) representing the cubes chosen in the lexicographically smallest solution with maximum number of cubes.Then, only if there is a solution, one more line follows containing $k_{m i n}$, the minimum number of cubes we can assign in the volume that will generate the two projections given in the input.After that, the next $k_{m i n}$ lines should contain triplets of numbers $x$, $y$, $z$ ($0 <= x < n$, $0 <= y < m$, $0 <= z < h$) representing the cubes in the lexicographically smallest solution with minimum number of cubes.
[samples]
## Note
A cube at coordinates $(x, y, z)$ will generate a shadow at line $x$ and column $y$ in the $n times m$ projection and line $x$ and column $z$ in the $n times h$ projection (indexed from $0$).
**Definitions**
Let $ n, k \in \mathbb{Z}^+ $ with $ 1 \leq n, k \leq 10^5 $.
Let $ M = (m_1, m_2, \dots, m_n) $ be Mahmoud's array.
Let $ B = (b_1, b_2, \dots, b_n) $ be Bashar's array.
**Constraints**
For all $ i \in \{1, \dots, n\} $:
$ 1 \leq m_i \leq 10^5 $,
$ 1 \leq b_i \leq 10^5 $.
**Objective**
Define a pair $ (i, j) $ with $ 1 \leq i < j \leq n $ as a *good pair* if:
$$
|m_i - m_j| \geq k \quad \text{(for Mahmoud)}, \quad \text{or} \quad |b_i - b_j| \geq k \quad \text{(for Bashar)}.
$$
Let $ P_M $ be the number of good pairs in $ M $, and $ P_B $ be the number of good pairs in $ B $.
Determine:
- If $ P_M > P_B $, output $ \text{"Mahmoud"} $,
- If $ P_B > P_M $, output $ \text{"Bashar"} $,
- If $ P_M = P_B $, output $ \text{"Draw"} $.