#include <bits/stdc++.h>
using namespace std;
const long long int MOD = 1000000007;
const long long BIG = 1446803456761533460;
const int Big = 336860180;
stringstream sss;
const long long int maxn = 1010;
long long int k, n, t, v;
bool ar[maxn][maxn];
void add(long long int a, long long int b) { ar[a][b] = ar[b][a] = true; }
void path(long long int a, long long int t) {
  add(1, ++n);
  for (long long int i = (0); i < (t); ++i) {
    add(n, n + 1);
    ++n;
  }
  add(a, n);
}
void two() {
  add(n + 1, v);
  add(n + 2, v);
  add(n + 3, n + 1);
  add(n + 3, n + 2);
  n += 3;
}
void make(long long int k) {
  if (k == 1) return;
  make(k / 2);
  two();
  v = n;
  if (k % 2) {
    path(v, t);
  }
  t += 2;
}
void MAIN() {
  cin >> k;
  n = 1, t = 0, v = 1;
  make(k);
  add(0, v);
  ++n;
  cout << n << '\n';
  for (long long int i = (0); i < (n); ++i) {
    for (long long int j = (0); j < (n); ++j) {
      cout << (ar[i][j] ? 'Y' : 'N');
    }
    cout << '\n';
  }
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  cout << fixed << setprecision(10);
  sss << R"(
6
    )";
  MAIN();
  return 0;
}

### Prompt

Your task is to create a Cpp solution to the following problem:

Fox Ciel wants to write a task for a programming contest. The task is: "You are given a simple undirected graph with n vertexes. Each its edge has unit length. You should calculate the number of shortest paths between vertex 1 and vertex 2."

Same with some writers, she wants to make an example with some certain output: for example, her birthday or the number of her boyfriend. Can you help her to make a test case with answer equal exactly to k?

Input

The first line contains a single integer k (1 ≤ k ≤ 109).

Output

You should output a graph G with n vertexes (2 ≤ n ≤ 1000). There must be exactly k shortest paths between vertex 1 and vertex 2 of the graph.

The first line must contain an integer n. Then adjacency matrix G with n rows and n columns must follow. Each element of the matrix must be 'N' or 'Y'. If Gij is 'Y', then graph G has a edge connecting vertex i and vertex j. Consider the graph vertexes are numbered from 1 to n.

The graph must be undirected and simple: Gii = 'N' and Gij = Gji must hold. And there must be at least one path between vertex 1 and vertex 2. It's guaranteed that the answer exists. If there multiple correct answers, you can output any of them. 

Examples

Input

2

Output

4
NNYY
NNYY
YYNN
YYNN

Input

9

Output

8
NNYYYNNN
NNNNNYYY
YNNNNYYY
YNNNNYYY
YNNNNYYY
NYYYYNNN
NYYYYNNN
NYYYYNNN

Input

1

Output

2
NY
YN

Note

In first example, there are 2 shortest paths: 1-3-2 and 1-4-2.

In second example, there are 9 shortest paths: 1-3-6-2, 1-3-7-2, 1-3-8-2, 1-4-6-2, 1-4-7-2, 1-4-8-2, 1-5-6-2, 1-5-7-2, 1-5-8-2.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long int MOD = 1000000007;
const long long BIG = 1446803456761533460;
const int Big = 336860180;
stringstream sss;
const long long int maxn = 1010;
long long int k, n, t, v;
bool ar[maxn][maxn];
void add(long long int a, long long int b) { ar[a][b] = ar[b][a] = true; }
void path(long long int a, long long int t) {
  add(1, ++n);
  for (long long int i = (0); i < (t); ++i) {
    add(n, n + 1);
    ++n;
  }
  add(a, n);
}
void two() {
  add(n + 1, v);
  add(n + 2, v);
  add(n + 3, n + 1);
  add(n + 3, n + 2);
  n += 3;
}
void make(long long int k) {
  if (k == 1) return;
  make(k / 2);
  two();
  v = n;
  if (k % 2) {
    path(v, t);
  }
  t += 2;
}
void MAIN() {
  cin >> k;
  n = 1, t = 0, v = 1;
  make(k);
  add(0, v);
  ++n;
  cout << n << '\n';
  for (long long int i = (0); i < (n); ++i) {
    for (long long int j = (0); j < (n); ++j) {
      cout << (ar[i][j] ? 'Y' : 'N');
    }
    cout << '\n';
  }
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  cout << fixed << setprecision(10);
  sss << R"(
6
    )";
  MAIN();
  return 0;
}

```