#include <bits/stdc++.h>
using namespace std;
const int INFint = 2147483647;
const long long INF = 9223372036854775807ll;
const long long MOD = 1000000009ll;
const long double EPS = 1e-9;
int a[111][111];
int main() {
  ios_base::sync_with_stdio(0);
  int k;
  cin >> k;
  int n;
  a[0][1] = a[1][0] = 1;
  for (n = 2; n < 101; n++) {
    if (!k) break;
    for (int i = 0; i < n; i++) {
      if (k < i) break;
      a[n][i] = a[i][n] = 1;
      k -= i;
    }
  }
  cout << n << endl;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) cout << a[i][j];
    cout << endl;
  }
  fprintf(stderr, "\nTIME = %lf\n", 1.0 * clock() / CLOCKS_PER_SEC);
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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 INFint = 2147483647;
const long long INF = 9223372036854775807ll;
const long long MOD = 1000000009ll;
const long double EPS = 1e-9;
int a[111][111];
int main() {
  ios_base::sync_with_stdio(0);
  int k;
  cin >> k;
  int n;
  a[0][1] = a[1][0] = 1;
  for (n = 2; n < 101; n++) {
    if (!k) break;
    for (int i = 0; i < n; i++) {
      if (k < i) break;
      a[n][i] = a[i][n] = 1;
      k -= i;
    }
  }
  cout << n << endl;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) cout << a[i][j];
    cout << endl;
  }
  fprintf(stderr, "\nTIME = %lf\n", 1.0 * clock() / CLOCKS_PER_SEC);
  return 0;
}

```