CodeForces

CodeForces - 233C

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.

Example
Input

1Output3011101110Input10Output50111110111110111110111110

#include <cstdio>#include <cstring>#include <iostream>#include <algorithm>#include <stack>using namespace std;int next[100010];char s[100010];int main(){    int n;    scanf("%d",&n);    int x=2;    int xx=0;    int map[110][110];    map[1][2]=map[2][1]=1;    for (int i=3;i<=100;i++){        x=max(x,i);        map[i][1]=map[1][i]=1;        for (int j=2;j<i;j++){            map[i][j]=map[j][i]=1;            xx+=j-1;            if (xx==n){                break;            }            else if(xx>n){                xx-=j-1;                map[i][j]=map[j][i]=0;                break;            }         }        if (xx==n){            break;        }    }    printf("%d\n",x);    for (int i=1;i<=x;i++){        for (int j=1;j<=x;j++){            if (j!=x)            printf("%d",map[i][j]);        else            printf("%d\n",map[i][j]);        }    }    return 0;}