#include <bits/stdc++.h>
using namespace std;
const int maxn = 1005;
bool g[maxn][maxn];
int Ke[maxn], Si[maxn], K, cnt;
void Add(int a, int b) { g[a][b] = g[b][a] = 1; }
void work(int x) {
  int c = 62 - 2 * x - 1;
  Add(Si[c], Ke[x]);
}
void do_it() {
  memset(g, 0, sizeof(g));
  Ke[0] = 1;
  cnt = 2;
  for (int i = 1; i < 33; ++i) {
    Add(cnt, cnt - 1);
    cnt++;
    Add(cnt, cnt - 2);
    cnt++;
    Add(cnt, cnt - 2);
    Add(cnt, cnt - 1);
    Ke[i] = cnt++;
  }
  int pre = 0;
  for (int i = 1; i < 65; ++i) {
    Add(cnt, pre);
    Si[i] = cnt;
    pre = cnt++;
  }
  for (int i = 0; i < 32; ++i)
    if ((K >> i) & 1) work(i);
}
int main() {
  while (scanf("%d", &K) != EOF) {
    do_it();
    printf("%d\n", cnt);
    for (int i = 0; i < cnt; ++i) {
      for (int j = 0; j < cnt; ++j) printf("%c", g[i][j] ? 'Y' : 'N');
      printf("\n");
    }
  }
  return 0;
}

### Prompt

Create a solution in cpp for 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 int maxn = 1005;
bool g[maxn][maxn];
int Ke[maxn], Si[maxn], K, cnt;
void Add(int a, int b) { g[a][b] = g[b][a] = 1; }
void work(int x) {
  int c = 62 - 2 * x - 1;
  Add(Si[c], Ke[x]);
}
void do_it() {
  memset(g, 0, sizeof(g));
  Ke[0] = 1;
  cnt = 2;
  for (int i = 1; i < 33; ++i) {
    Add(cnt, cnt - 1);
    cnt++;
    Add(cnt, cnt - 2);
    cnt++;
    Add(cnt, cnt - 2);
    Add(cnt, cnt - 1);
    Ke[i] = cnt++;
  }
  int pre = 0;
  for (int i = 1; i < 65; ++i) {
    Add(cnt, pre);
    Si[i] = cnt;
    pre = cnt++;
  }
  for (int i = 0; i < 32; ++i)
    if ((K >> i) & 1) work(i);
}
int main() {
  while (scanf("%d", &K) != EOF) {
    do_it();
    printf("%d\n", cnt);
    for (int i = 0; i < cnt; ++i) {
      for (int j = 0; j < cnt; ++j) printf("%c", g[i][j] ? 'Y' : 'N');
      printf("\n");
    }
  }
  return 0;
}

```