Problem Statement

Given are a positive integer N and a sequence of length 2^N consisting of 0s and 1s: $A_0,A_1,\ldots,A_{2^N-1}$.
Determine whether there exists a closed curve C that satisfies the condition below for all $2^N sets S \subseteq$ ${0,1,\ldots,N-1$ }. If the answer is yes, construct one such closed curve.

• Let $x = \sum_{i \in$ S} 2^i and B_S be the set of points ${ (i+0.5,0.5) | i \in$ S }.
• If there is a way to continuously move the closed curve C without touching B_S so that every point on the closed curve has a negative y-coordinate, A_x = 1.
• If there is no such way, A_x = 0.

For instruction on printing a closed curve, see Output below.

Input

Input is given from Standard Input in the following format:
N
$A_0A_1 \cdots A_{2^N-1}$

Output

If there is no closed curve that satisfies the condition, print Impossible.
If such a closed curve exists, print Possible in the first line.
Then, print one such curve in the following format:
L
x_0 y_0
x_1 y_1
:
x_L y_L

This represents the closed polyline that passes $(x_0,y_0),(x_1,y_1),\ldots,(x_L,y_L)$ in this order.
Here, all of the following must be satisfied:

• $0 \leq x_i \leq N, 0 \leq y_i \leq 1$, and x_i, y_i are integers. $(0 \leq i \leq L)$
• $|x_i-x_{i+1}| + |y_i-y_{i+1}| = 1. (0 \leq i \leq L-1)$
• (x_0,y_0) = (x_L,y_L).

Additionally, the length of the closed curve L must satisfy $0 \leq L \leq 250000$.
It can be proved that, if there is a closed curve that satisfies the condition in Problem Statement, there is also a closed curve that can be expressed in this format.

Constraints

• $1 \leq N \leq 8$
• $A_i = 0,1 \quad (0 \leq i \leq 2^N-1)$
• A_0 = 1

Sample Input 1

1
10

Sample Output 1

Possible
4
0 0
0 1
1 1
1 0
0 0

When $S = \emptyset$, we can move this curve so that every point on it has a negative y-coordinate.

When S = {0}, we cannot do so.

Sample Input 2

2
1000

Sample Output 2

Possible
6
1 0
2 0
2 1
1 1
0 1
0 0
1 0

The output represents the following curve:

Sample Input 3

2
1001

Sample Output 3

Impossible

Sample Input 4

1
11

Sample Output 4

Possible
0
1 1

见题面 Input 部分

见题面 Output 部分