#include <bits/stdc++.h>
#define fi first
#define se second
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define rrep(i,n) for(int i = 1; i <= (n); ++i)
#define drep(i,n) for(int i = (n)-1; i >= 0; --i)
#define srep(i,s,t) for (int i = s; i < t; ++i)
#define rng(a) a.begin(),a.end()
#define rrng(a) a.rbegin(),a.rend()
#define maxs(x,y) (x = max(x,y))
#define mins(x,y) (x = min(x,y))
#define limit(x,l,r) max(l,min(x,r))
#define lims(x,l,r) (x = max(l,min(x,r)))
#define isin(x,l,r) ((l) <= (x) && (x) < (r))
#define pb push_back
#define eb emplace_back
#define sz(x) (int)(x).size()
#define pcnt __builtin_popcountll
#define uni(x) x.erase(unique(rng(x)),x.end())
#define snuke srand((unsigned)clock()+(unsigned)time(NULL));
#define show(x) cout<<#x<<" = "<<x<<endl;
#define PQ(T) priority_queue<T,v(T),greater<T> >
#define bn(x) ((1<<x)-1)
#define dup(x,y) (((x)+(y)-1)/(y))
#define newline puts("")
#define v(T) vector<T>
#define vv(T) v(v(T))
using namespace std;
typedef long long int ll;
typedef unsigned uint;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef tuple<int,int,int> T;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<P> vp;
typedef vector<T> vt;
inline int getInt() { int x; scanf("%d",&x); return x;}
template<typename T>inline istream& operator>>(istream&i,v(T)&v)
{rep(j,sz(v))i>>v[j];return i;}
template<typename T>string join(const v(T)&v)
{stringstream s;rep(i,sz(v))s<<' '<<v[i];return s.str().substr(1);}
template<typename T>inline ostream& operator<<(ostream&o,const v(T)&v)
{if(sz(v))o<<join(v);return o;}
template<typename T1,typename T2>inline istream& operator>>(istream&i,pair<T1,T2>&v)
{return i>>v.fi>>v.se;}
template<typename T1,typename T2>inline ostream& operator<<(ostream&o,const pair<T1,T2>&v)
{return o<<v.fi<<","<<v.se;}
template<typename T>inline ll suma(const v(T)& a) { ll res(0); for (auto&& x : a) res += x; return res;}
const double eps = 1e-10;
const ll LINF = 1001002003004005006ll;
const int INF = 1001001001;
#define dame { puts("Impossible"); return 0;}
#define yn {puts("Yes");}else{puts("No");}
const int MX = 200005;

vp f(vi a) {
  int x = a.back();
  if (sz(a) == 1) {
    vp res;
    rep(i,x+2) res.eb(i,0);
    res.eb(x+1,1);
    res.eb(x,1);
    drep(i,x+1) res.eb(i,0);
    res.eb(0,1);
    return res;
  }
  a.pop_back();
  rep(i,sz(a)) a[i] -= x+1;
  vp d = f(a);
  rep(i,sz(d)) d[i].fi += x+1;
  vp res;
  rep(i,x+1) res.eb(i,0);
  res.insert(res.end(), rng(d));
  res.eb(x+1,0);
  res.eb(x,0);
  res.eb(x,1);
  reverse(rng(d));
  res.insert(res.end(), rng(d));
  res.eb(x+1,1);
  res.eb(x,1);
  drep(i,x+1) res.eb(i,0);
  res.eb(0,1);
  return res;
}

int main() {
  int n;
  scanf("%d",&n);
  string st;
  cin>>st;
  int n2 = 1<<n;
  vi a(n2);
  rep(i,n2) a[i] = st[i]-'0';
  rep(i,n2) a[i] ^= 1;
  rep(i,n2) {
    if (a[i]) continue;
    for (int j = i;; j = (j-1)&i) {
      if (a[j]) dame;
      if (!j) break;
    }
  }
  if (a[0]) dame;
  cout<<"Possible"<<endl;
  vp ans;
  rep(i,n2) {
    if (!a[i]) continue;
    vi s;
    rep(j,n) if (i>>j&1) s.pb(j);
    reverse(rng(s));
    vp now = f(s);
    ans.insert(ans.end(), rng(now));
  }
  ans.eb(0,0);
  cout<<sz(ans)-1<<endl;
  for (P p : ans) {
    cout<<p.fi<<" "<<p.se<<endl;
  }
  return 0;
}





















### Prompt

In cpp, your task is to solve the following 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

### Response

```cpp
#include <bits/stdc++.h>
#define fi first
#define se second
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define rrep(i,n) for(int i = 1; i <= (n); ++i)
#define drep(i,n) for(int i = (n)-1; i >= 0; --i)
#define srep(i,s,t) for (int i = s; i < t; ++i)
#define rng(a) a.begin(),a.end()
#define rrng(a) a.rbegin(),a.rend()
#define maxs(x,y) (x = max(x,y))
#define mins(x,y) (x = min(x,y))
#define limit(x,l,r) max(l,min(x,r))
#define lims(x,l,r) (x = max(l,min(x,r)))
#define isin(x,l,r) ((l) <= (x) && (x) < (r))
#define pb push_back
#define eb emplace_back
#define sz(x) (int)(x).size()
#define pcnt __builtin_popcountll
#define uni(x) x.erase(unique(rng(x)),x.end())
#define snuke srand((unsigned)clock()+(unsigned)time(NULL));
#define show(x) cout<<#x<<" = "<<x<<endl;
#define PQ(T) priority_queue<T,v(T),greater<T> >
#define bn(x) ((1<<x)-1)
#define dup(x,y) (((x)+(y)-1)/(y))
#define newline puts("")
#define v(T) vector<T>
#define vv(T) v(v(T))
using namespace std;
typedef long long int ll;
typedef unsigned uint;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef tuple<int,int,int> T;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<P> vp;
typedef vector<T> vt;
inline int getInt() { int x; scanf("%d",&x); return x;}
template<typename T>inline istream& operator>>(istream&i,v(T)&v)
{rep(j,sz(v))i>>v[j];return i;}
template<typename T>string join(const v(T)&v)
{stringstream s;rep(i,sz(v))s<<' '<<v[i];return s.str().substr(1);}
template<typename T>inline ostream& operator<<(ostream&o,const v(T)&v)
{if(sz(v))o<<join(v);return o;}
template<typename T1,typename T2>inline istream& operator>>(istream&i,pair<T1,T2>&v)
{return i>>v.fi>>v.se;}
template<typename T1,typename T2>inline ostream& operator<<(ostream&o,const pair<T1,T2>&v)
{return o<<v.fi<<","<<v.se;}
template<typename T>inline ll suma(const v(T)& a) { ll res(0); for (auto&& x : a) res += x; return res;}
const double eps = 1e-10;
const ll LINF = 1001002003004005006ll;
const int INF = 1001001001;
#define dame { puts("Impossible"); return 0;}
#define yn {puts("Yes");}else{puts("No");}
const int MX = 200005;

vp f(vi a) {
  int x = a.back();
  if (sz(a) == 1) {
    vp res;
    rep(i,x+2) res.eb(i,0);
    res.eb(x+1,1);
    res.eb(x,1);
    drep(i,x+1) res.eb(i,0);
    res.eb(0,1);
    return res;
  }
  a.pop_back();
  rep(i,sz(a)) a[i] -= x+1;
  vp d = f(a);
  rep(i,sz(d)) d[i].fi += x+1;
  vp res;
  rep(i,x+1) res.eb(i,0);
  res.insert(res.end(), rng(d));
  res.eb(x+1,0);
  res.eb(x,0);
  res.eb(x,1);
  reverse(rng(d));
  res.insert(res.end(), rng(d));
  res.eb(x+1,1);
  res.eb(x,1);
  drep(i,x+1) res.eb(i,0);
  res.eb(0,1);
  return res;
}

int main() {
  int n;
  scanf("%d",&n);
  string st;
  cin>>st;
  int n2 = 1<<n;
  vi a(n2);
  rep(i,n2) a[i] = st[i]-'0';
  rep(i,n2) a[i] ^= 1;
  rep(i,n2) {
    if (a[i]) continue;
    for (int j = i;; j = (j-1)&i) {
      if (a[j]) dame;
      if (!j) break;
    }
  }
  if (a[0]) dame;
  cout<<"Possible"<<endl;
  vp ans;
  rep(i,n2) {
    if (!a[i]) continue;
    vi s;
    rep(j,n) if (i>>j&1) s.pb(j);
    reverse(rng(s));
    vp now = f(s);
    ans.insert(ans.end(), rng(now));
  }
  ans.eb(0,0);
  cout<<sz(ans)-1<<endl;
  for (P p : ans) {
    cout<<p.fi<<" "<<p.se<<endl;
  }
  return 0;
}





















```