Problem: 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.

Constraints

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

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.

Examples

Input

1
10


Output

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


Input

2
1000


Output

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


Input

2
1001


Output

Impossible


Input

1
11


Output

Possible
0
1 1

Solution (in PYTHON3):

Solution:
n = int(input())
a = [int(x) for x in input()]

holes = []

for i in range(2**n):
    if a[i] == 1:
        continue
    for j in range(i+1, 2**n):
        if (j | i) == j and a[j] == 1:
            print("Impossible")
            exit()
    if any((k | i) == i for k in holes):
        continue
    else:
        holes.append(i)

print("Possible")
if len(holes) == 0:
    print(0)
    print(1, 1)
    exit()

clockwise = []

for i in range(n):
    locus = []
    for j in range(i+1):
        locus.append((j, 0))
    locus += [(i, 1), (i+1, 1), (i+1, 0)]
    for j in range(i, -1, -1):
        locus.append((j, 0))
    clockwise.append(locus)

m = len(holes)
roops = []

for i in range(m):
    x = holes[i]
    curve = []
    is_first = True
    for j in range(n):
        if (x >> j) & 1 and is_first:
            curve += clockwise[j]
            is_first = False
        elif (x >> j) & 1:
            curve = curve + clockwise[j] + curve[::-1] + clockwise[j][::-1]
    roops.append(curve)

ans = []
for x in roops:
    ans += x

L = -1
for i, x in enumerate(ans):
    if i > 0 and ans[i] == ans[i-1]:
        continue
    else:
        L += 1

print(L)
for i, x in enumerate(ans):
    if i > 0 and ans[i] == ans[i-1]:
        continue
    else:
        print(*x)