#include <bits/stdc++.h>
using namespace std;
const int INF = 2147483647;
const long long LLINF = 9223372036854775807LL;
const int maxn = 100;
int a[maxn][maxn];
int k;
void dfs(int cnt) {
  if (cnt == k) {
    printf("%d\n", 100);
    for (int i = 0; i < maxn; ++i) {
      for (int j = 0; j < maxn; ++j) {
        printf("%d", a[i][j]);
      }
      printf("\n");
    }
    exit(0);
  }
  if (cnt > k) return;
  for (int iter = 0; iter < 3; ++iter) {
    int fr = 0;
    int to = 1;
    while (fr == to || a[fr][to]) {
      fr = rand() % 100;
      to = rand() % 100;
    }
    a[fr][to] = 1;
    a[to][fr] = 1;
    int cur = 0;
    for (int i = 0; i < maxn; ++i)
      if (i != fr && i != to && a[i][fr] && a[i][to]) cur++;
    dfs(cnt + cur);
    a[fr][to] = 0;
    a[to][fr] = 0;
  }
}
int main() {
  scanf("%d", &k);
  dfs(0);
  return 0;
}

### Prompt

Your challenge is to write a Cpp solution to the following problem:

John Doe started thinking about graphs. After some thought he decided that he wants to paint an undirected graph, containing exactly k cycles of length 3. 

A cycle of length 3 is an unordered group of three distinct graph vertices a, b and c, such that each pair of them is connected by a graph edge. 

John has been painting for long, but he has not been a success. Help him find such graph. Note that the number of vertices there shouldn't exceed 100, or else John will have problems painting it.

Input

A single line contains an integer k (1 ≤ k ≤ 105) — the number of cycles of length 3 in the required graph.

Output

In the first line print integer n (3 ≤ n ≤ 100) — the number of vertices in the found graph. In each of next n lines print n characters "0" and "1": the i-th character of the j-th line should equal "0", if vertices i and j do not have an edge between them, otherwise it should equal "1". Note that as the required graph is undirected, the i-th character of the j-th line must equal the j-th character of the i-th line. The graph shouldn't contain self-loops, so the i-th character of the i-th line must equal "0" for all i.

Examples

Input

1


Output

3
011
101
110


Input

10


Output

5
01111
10111
11011
11101
11110

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int INF = 2147483647;
const long long LLINF = 9223372036854775807LL;
const int maxn = 100;
int a[maxn][maxn];
int k;
void dfs(int cnt) {
  if (cnt == k) {
    printf("%d\n", 100);
    for (int i = 0; i < maxn; ++i) {
      for (int j = 0; j < maxn; ++j) {
        printf("%d", a[i][j]);
      }
      printf("\n");
    }
    exit(0);
  }
  if (cnt > k) return;
  for (int iter = 0; iter < 3; ++iter) {
    int fr = 0;
    int to = 1;
    while (fr == to || a[fr][to]) {
      fr = rand() % 100;
      to = rand() % 100;
    }
    a[fr][to] = 1;
    a[to][fr] = 1;
    int cur = 0;
    for (int i = 0; i < maxn; ++i)
      if (i != fr && i != to && a[i][fr] && a[i][to]) cur++;
    dfs(cnt + cur);
    a[fr][to] = 0;
    a[to][fr] = 0;
  }
}
int main() {
  scanf("%d", &k);
  dfs(0);
  return 0;
}

```