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.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
vector<vector<int> > adj(1000);
string MAT[1000];
void addEdge(int u, int v) {
  adj[u].push_back(v);
  adj[v].push_back(u);
}
int main() {
  int N;
  cin >> N;
  int S = 0, T = 1;
  int ID = 2;
  int L = 30;
  vector<vector<int> > V(L);
  for (int i = 0; i < L; ++i) {
    V[i].push_back(ID++);
    V[i].push_back(ID++);
  }
  for (int i = 0; i + 1 < L; ++i) {
    addEdge(V[i][0], V[i + 1][0]);
    addEdge(V[i][0], V[i + 1][1]);
    addEdge(V[i][1], V[i + 1][0]);
    addEdge(V[i][1], V[i + 1][1]);
  }
  addEdge(V[L - 1][0], T);
  addEdge(V[L - 1][1], T);
  for (int i = 0; i < L; ++i) {
  }
  for (int i = 0; i <= L; ++i) {
    if ((1 << i) & N) {
      int C = L - i;
      int LI = ID++;
      addEdge(S, LI);
      for (int j = 0; j < C; ++j) {
        int nID = ID++;
        addEdge(LI, nID);
        LI = nID;
      }
      if (i == 0)
        addEdge(LI, T);
      else {
        addEdge(LI, V[C][0]);
        addEdge(LI, V[C][1]);
      }
    }
  }
  for (int i = 0; i < ID; ++i) {
    MAT[i] = string(ID, 'N');
  }
  cout << ID << endl;
  for (int i = 0; i < ID; ++i) {
    for (int j = 0; j < adj[i].size(); ++j) {
      MAT[i][adj[i][j]] = 'Y';
    }
    cout << MAT[i] << endl;
  }
}