#include <bits/stdc++.h>
using namespace std;
int E[2005][2005];
vector<int> LAYER[35];
void add_edge(int from, int to) { E[from][to] = E[to][from] = 1; }
int main() {
  int n;
  cin >> n;
  if (n == 1) {
    cout << 2 << endl;
    cout << "NY" << endl;
    cout << "YN" << endl;
    return 0;
  }
  int vertex = 3;
  int source = 1;
  int dest = 2;
  int i;
  int target_dist;
  int layer = 0;
  for (i = 31; i >= 0; i--) {
    if (n & (1 << i)) {
      int aux = i - 1;
      target_dist = i;
      add_edge(source, vertex);
      add_edge(source, vertex + 1);
      while (aux--) {
        add_edge(vertex, vertex + 2);
        add_edge(vertex, vertex + 3);
        add_edge(vertex + 1, vertex + 2);
        add_edge(vertex + 1, vertex + 3);
        vertex += 2;
        LAYER[layer].push_back(vertex);
        LAYER[layer].push_back(vertex + 1);
        layer++;
      }
      add_edge(vertex, dest);
      add_edge(vertex + 1, dest);
      vertex += 2;
      i--;
      break;
    }
  }
  for (; i >= 0; i--) {
    if (n & (1 << i)) {
      add_edge(source, vertex);
      int target_layer = layer - 1;
      int need = (1 << i);
      int pow = 1;
      bool connect_two = false;
      while (true) {
        if (pow == need || (pow << 1) == need) {
          if ((pow << 1) == need) connect_two = true;
          break;
        }
        target_layer--;
        pow <<= 1;
      }
      for (int j = 1; j <= target_layer; j++) {
        add_edge(vertex, vertex + 1);
        vertex++;
      }
      if (connect_two) {
        add_edge(vertex, LAYER[target_layer][0]);
        add_edge(vertex, LAYER[target_layer][1]);
      } else {
        add_edge(vertex, LAYER[target_layer][0]);
      }
      vertex++;
    }
  }
  cout << vertex << endl;
  for (int i = 1; i <= vertex; i++) {
    for (int j = 1; j <= vertex; j++) {
      if (E[i][j])
        cout << 'Y';
      else
        cout << 'N';
    }
    cout << endl;
  }
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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;
int E[2005][2005];
vector<int> LAYER[35];
void add_edge(int from, int to) { E[from][to] = E[to][from] = 1; }
int main() {
  int n;
  cin >> n;
  if (n == 1) {
    cout << 2 << endl;
    cout << "NY" << endl;
    cout << "YN" << endl;
    return 0;
  }
  int vertex = 3;
  int source = 1;
  int dest = 2;
  int i;
  int target_dist;
  int layer = 0;
  for (i = 31; i >= 0; i--) {
    if (n & (1 << i)) {
      int aux = i - 1;
      target_dist = i;
      add_edge(source, vertex);
      add_edge(source, vertex + 1);
      while (aux--) {
        add_edge(vertex, vertex + 2);
        add_edge(vertex, vertex + 3);
        add_edge(vertex + 1, vertex + 2);
        add_edge(vertex + 1, vertex + 3);
        vertex += 2;
        LAYER[layer].push_back(vertex);
        LAYER[layer].push_back(vertex + 1);
        layer++;
      }
      add_edge(vertex, dest);
      add_edge(vertex + 1, dest);
      vertex += 2;
      i--;
      break;
    }
  }
  for (; i >= 0; i--) {
    if (n & (1 << i)) {
      add_edge(source, vertex);
      int target_layer = layer - 1;
      int need = (1 << i);
      int pow = 1;
      bool connect_two = false;
      while (true) {
        if (pow == need || (pow << 1) == need) {
          if ((pow << 1) == need) connect_two = true;
          break;
        }
        target_layer--;
        pow <<= 1;
      }
      for (int j = 1; j <= target_layer; j++) {
        add_edge(vertex, vertex + 1);
        vertex++;
      }
      if (connect_two) {
        add_edge(vertex, LAYER[target_layer][0]);
        add_edge(vertex, LAYER[target_layer][1]);
      } else {
        add_edge(vertex, LAYER[target_layer][0]);
      }
      vertex++;
    }
  }
  cout << vertex << endl;
  for (int i = 1; i <= vertex; i++) {
    for (int j = 1; j <= vertex; j++) {
      if (E[i][j])
        cout << 'Y';
      else
        cout << 'N';
    }
    cout << endl;
  }
  return 0;
}

```