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>
#include<cstring>
#define rep(i, s, t) for(i = s; i <= t; ++i)
#define dep(i, s, t) for(i = s; i >= t; --i)

using namespace std;

const int N = 130, M = N*N;
int n, m;
int d[15][15], p[N][N];
int x[M], y[M], v[M], cnt;

int dis(int A, int B) {
	int ret = 101, i, j;
	rep(i, 0, 100)
		rep(j, 0, 100)
			if(p[i][j] >= 0) ret = min(ret, i*A + j*B + p[i][j]);
	return ret;
}

int main() {
	int i, j, k, A, B; bool f = 1;
	scanf("%d%d", &n, &m);
	rep(i, 1, n) rep(j, 1, m) scanf("%d", &d[i][j]);
	rep(A, 0, 100)
		rep(B, 0, 100) {
			p[A][B] = -100;
			rep(i, 1, n)
				rep(j, 1, m) {
					p[A][B] = max(p[A][B], d[i][j] - i*A - j*B);
				}
			if(p[A][B] >= 0) {
				++cnt;
				x[cnt] = A+1; y[cnt] = B+102; v[cnt] = p[A][B];				
			}
		}
		
	rep(i, 1, n) rep(j, 1, m) 
	if(dis(i, j) != d[i][j]) {puts("Impossible"); return 0;}
		
	
	puts("Possible");
	printf("%d %d\n", 202, cnt+200);
	rep(i, 1, cnt) printf("%d %d %d\n", x[i], y[i], v[i]);
	rep(i, 2, 101) printf("%d %d X\n", i-1, i);
	rep(i, 103, 202) printf("%d %d Y\n", i, i-1);
	puts("1 102");
	return 0;
}