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: Wrong Answer)

#include<iostream>
#include<string>
#include<cmath>
#include<queue>
#include<map>
#include<set>
#include<list>
#include<iomanip>
#include<vector>
#include<functional>
#include<algorithm>
#include<cstdio>
#include<random>
#include<ctime>
#include<cstdlib>
#include<unordered_map>
#include<string.h>
#include<iostream>
#define p pair<int,int>
#define P pair<int,p>
using namespace std;

vector<P>V;
int k[10][10];
signed main() {
	int a, b; cin >> a >> b;
	for (int i = 0; i < a; i++) {
		for (int j = 0; j < b; j++) {
			cin >> k[i][j];
		}
	}
	for (int i = 0; i < 100; i++) {
		V.push_back({ -1,{i,i + 1} });
	}
	for (int i = 0; i < 100; i++) {
		V.push_back({ -2,{ 101+i,i + 102 } });
	}
	for (int i = 0; i <= 100; i++) {
		for (int j = 101; j <= 201; j++) {
			int MAX = 0;//余裕の最大値
			for (int k = 0; k < a; k++) {
				for (int l = 0; l < b; l++) {
					MAX = max(MAX, ::k[k][l] - i*(k + 1) - (201 - j)*(l + 1));
				}
			}
			V.push_back({ MAX,{i,j} });
		}
	}
	for (int i = 0; i < a; i++) {
		for (int j = 0; j < b; j++) {

		}
	}
	cout << 202 << " " << 101 * 101 << endl;
	for (P i : V) {
		if (i.first == -1) {
			cout << i.second.first << " " << i.second.second << "  X" << endl;
		}
		else if (i.first == -2) {
			cout << i.second.first << " " << i.second.second << "  Y" <<endl;
		}
		else {

			cout << i.second.first << " " << i.second.second << " " << i.first << endl;
		}
	}
	cout << 1 << " " << 202 << endl;
}