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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <cstdio>
#include <algorithm>
#define FOR(i, l, r) for(int i = l; i <= r; ++i)

using namespace std;

const int N = 110;

int n, m, d[N][N], f[N][N], dd[N][N];

int main()
{
    scanf("%d%d", &n, &m);
    FOR(i, 1, n) FOR(j, 1, m) scanf("%d", &d[i][j]);
    FOR(i, 0, 100) FOR(j, 0, 100) FOR(ii, 1, n) FOR(jj, 1, m)
        f[i][j] = max(f[i][j], d[ii][jj] - i * ii - j * jj);
    FOR(ii, 1, n) FOR(jj, 1, m)
    {
        dd[ii][jj] = 1e9;
        FOR(i, 0, 100) FOR(j, 0, 100)
            dd[ii][jj] = min(dd[ii][jj], i * ii + j * jj + f[i][j]);
        if (dd[ii][jj] != d[ii][jj]) {puts("Impossible"); return 0;}
    }
    puts("Possible"); puts("202 10401");
    FOR(i, 1, 100) printf("%d %d X\n", i, i + 1);
    FOR(i, 102, 201) printf("%d %d Y\n", i, i + 1);
    FOR(i, 0, 100) FOR(j, 0, 100) printf("%d %d %d\n", i + 1, 202 - j, f[i][j]);
    puts("1 202");
    return 0;
}