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:
res = []

n = int(input())
a = [int(c) for c in input()]

def solve():
    if a[0] == 0:
        return False
    for x in range(1, 2**n):
        s = list(filter(lambda i: (x >> i) & 1, range(n)))
        xl = [(x >> i) & 1 for i in range(n)]
        if a[x] == 0:
            for d in s:
                y = x ^ (1 << d)
                if a[y] == 1:
                    break
            else:
                continue
            def move_ceiling(r, dest):
                i, j = r[-1]
                if i < dest:
                    for i in range(i, dest):
                        if xl[i] == 0 and j == 1:
                            r.append((i, 0))
                            j = 0
                        elif xl[i] == 1 and j == 0:
                            r.append((i, 1))
                            j = 1
                        r.append((i + 1, j))
                else:
                    for i in range(i, dest, -1):
                        if xl[i - 1] == 0 and j == 1:
                            r.append((i, 0))
                            j = 0
                        elif xl[i - 1] == 1 and j == 0:
                            r.append((i, 1))
                            j = 1
                        r.append((i - 1, j))
                return r
            def move_floor(r, dest):
                i, j = r[-1]
                if j == 1:
                    r.append((i, 0))
                for i in range(i + 1, dest + 1) if i < dest else range(i - 1, dest - 1, -1):
                    r.append((i, 0))
                return r
            r = [(s[0] + 1, 1), (s[0], 1), (s[0], 0), (s[0] + 1, 0)]
            cur = s[0] + 1
            for d in s[1:]:
                r0 = [(d + 1, 1)] if cur == d else move_ceiling([(d + 1, 1)], cur)
                r1 = move_ceiling(r.copy(), d + 1)
                r1 = move_floor(r1, cur)
                r1.pop()
                r2 = list(reversed(r))
                r2 = move_floor(r2, d + 1)
                r = r0 + r1 + r2
                cur = d + 1
            r = move_floor(r, n)
            r.reverse()
            r = move_floor(r, n)
            r.pop()
            res.append(r)
        else:
            for d in s:
                y = x ^ (1 << d)
                if a[y] != 1:
                    return False
    return True

if __name__ == '__main__':
    if solve():
        print('Possible')
        r = [(i, j) for r in res for i, j in r]
        r.append((n, 0))
        print(len(r) - 1)
        for i, j in r:
            print(i, j)
    else:
        print('Impossible')