Problem:
Score : 900 points

Problem Statement

AtCoDeer the deer wants a directed graph that satisfies the following conditions:

The number of vertices, N, is at most 300.

There must not be self-loops or multiple edges.

The vertices are numbered from 1 through N.

Each edge has either an integer weight between 0 and 100 (inclusive), or a label X or Y.

For every pair of two integers (x,y) such that 1 ≤ x ≤ A, 1 ≤ y ≤ B,
the shortest distance from Vertex S to Vertex T in the graph where the edges labeled X have the weight x and the edges labeled Y have the weight y, is d_{x,y}.

Construct such a graph (and a pair of S and T) for him, or report that it does not exist.
Refer to Output section for output format.

Constraints

1 ≤ A,B ≤ 10

1 ≤ d_{x,y} ≤ 100 (1 ≤ x ≤ A, 1 ≤ y ≤ B)

All input values are integers.

Input

Input is given from Standard Input in the following format:

A B
d_{1,1} d_{1,2} .. d_{1,B}
d_{2,1} d_{2,2} .. d_{2,B}
:
d_{A,1} d_{A,2} .. d_{A,B}

Output

If no graph satisfies the condition, print Impossible.

If there exists a graph that satisfies the condition, print Possible in the first line.
Then, in the subsequent lines, print the constructed graph in the following format:

N M
u_1 v_1 c_1
u_2 v_2 c_2
:
u_M v_M c_M
S T

Here, M is the number of the edges, and u_i, v_i, c_i represent edges as follows: there is an edge from Vertex u_i to Vertex v_i whose weight or label is c_i.

Also refer to Sample Outputs.

Sample Input 1

2 3
1 2 2
1 2 3

Sample Output 1

Possible
3 4
1 2 X
2 3 1
3 2 Y
1 3 Y
1 3

Sample Input 2

1 3
100 50 1

Sample Output 2

Impossible

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

A, B = gets.split.map(&:to_i)
ds = []
(1..A).each do |i|
    ds[i] = [nil] + gets.split.map(&:to_i)
end

fs = Array.new(101){Array.new(101, 0)}
(0..100).each do |a|
    (0..100).each do |b|
        (1..A).each do |x|
            (1..B).each do |y|
                val = ds[x][y] - x*a - y*b
                fs[a][b] = val if fs[a][b] < val
            end
        end
    end
end

(1..A).each do |x|
    (1..B).each do |y|
        result = 10**10
        (0..100).each do |a|
            (0..100).each do |b|
                val = x*a+y*b+fs[a][b]
                result = val if result > val
            end
        end
        if ds[x][y] != result
            puts 'Impossible'
            exit
        end
    end
end

N = 202
S, T = 1, 202
M = 200 + 101 ** 2

puts 'Possible'
puts [N, M].join(' ')
(1..100).each do |i|
    puts [i, i+1, 'X'].join(' ')
end
(101..201).each do |i|
    puts [i, i+1, 'Y'].join(' ')
end
(0..100).each do |a|
    (0..100).each do |b|
        puts [S+a, T-b, fs[a][b]].join(' ')
    end
end
puts [S, T].join(' ')