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;
const int INF = 1E9;
const long double eps = 1e-7;
int n, nn, vertexes, maxst;
bool isst[31];
int id[31], needway[31];
vector<vector<int> > g;
vector<int> emp;
void addedge(int v, int w) {
  g[v].push_back(w);
  g[w].push_back(v);
}
void gen(int len) {
  vertexes = 2;
  int last = 0;
  g.push_back(emp);
  g.push_back(emp);
  for (int i = 0; i < len; i++) {
    g.push_back(emp);
    g.push_back(emp);
    g.push_back(emp);
    addedge(last, vertexes);
    addedge(last, vertexes + 1);
    addedge(vertexes, vertexes + 2);
    addedge(vertexes + 1, vertexes + 2);
    last = vertexes + 2;
    id[len - i - 1] = last;
    needway[len - i - 1] = (i + 1) * 2;
    vertexes += 3;
  }
  addedge(vertexes - 1, 1);
  for (int i = len - 1; i >= 0; i--) {
    if (isst[i]) {
      int iid = id[i];
      last = 0;
      for (int j = 0; j < int(needway[i] - 1); j++) {
        g.push_back(emp);
        addedge(last, vertexes);
        last = vertexes;
        vertexes++;
      }
      addedge(last, iid);
    }
  }
}
int main() {
  cin >> n;
  nn = n;
  maxst = 0;
  for (int i = 0; i < 31; i++) {
    if (nn & 1) {
      maxst = i;
      isst[i] = 1;
    }
    nn >>= 1;
  }
  if (n == 1) {
    vertexes = 2;
    g.resize(2);
    g[0].push_back(1);
    g[1].push_back(0);
  } else {
    gen(maxst);
  }
  cout << vertexes << '\n';
  string s;
  for (int i = 0; i < int(vertexes); i++) s += ' ';
  for (int i = 0; i < int(vertexes); i++) {
    for (int j = 0; j < int(vertexes); j++) s[j] = 'N';
    for (int j = 0; j < int(g[i].size()); j++) s[g[i][j]] = 'Y';
    cout << s << '\n';
  }
  return 0;
}