Problem: Diverta City is a new city consisting of N towns numbered 1, 2, ..., N.

The mayor Ringo is planning to connect every pair of two different towns with a bidirectional road. The length of each road is undecided.

A Hamiltonian path is a path that starts at one of the towns and visits each of the other towns exactly once. The reversal of a Hamiltonian path is considered the same as the original Hamiltonian path.

There are N! / 2 Hamiltonian paths. Ringo wants all these paths to have distinct total lengths (the sum of the lengths of the roads on a path), to make the city diverse.

Find one such set of the lengths of the roads, under the following conditions:

* The length of each road must be a positive integer.
* The maximum total length of a Hamiltonian path must be at most 10^{11}.

Constraints

* N is a integer between 2 and 10 (inclusive).

Input

Input is given from Standard Input in the following format:


N


Output

Print a set of the lengths of the roads that meets the objective, in the following format:


w_{1, 1} \ w_{1, 2} \ w_{1, 3} \ ... \ w_{1, N}
w_{2, 1} \ w_{2, 2} \ w_{2, 3} \ ... \ w_{2, N}
:  :     :
w_{N, 1} \ w_{N, 2} \ w_{N, 3} \ ... \ w_{N, N}


where w_{i, j} is the length of the road connecting Town i and Town j, which must satisfy the following conditions:

* w_{i, i} = 0
* w_{i, j} = w_{j, i} \ (i \neq j)
* 1 \leq w_{i, j} \leq 10^{11} \ (i \neq j)



If there are multiple sets of lengths of the roads that meet the objective, any of them will be accepted.

Examples

Input

3


Output

0 6 15
6 0 21
15 21 0


Input

4


Output

0 111 157 193
111 0 224 239
157 224 0 258
193 239 258 0

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;

#define nn 14
#define ll long long 
ll road[nn][nn];
ll n;
ll rati[]={1,2,4,7,12,20,29,38,52,73};
ll M;
void outprint(){
	for(int i=0;i<n;i++){
		for(int j=0;j<n;j++){
			printf("%lld ",road[i][j]); 
		}
		puts("");
	}
	exit(0);
}

ll id[nn];
void solve(ll m){
	for(int i=0;i<m;i++) id[i]=i;
	do{
		ll ans=0;
		for(int i=0;i<m;i++) ans+=road[id[i]][id[(i+1)%m]];
		M=max(M,ans);
	}while(next_permutation(id,id+m));
}
int main(){
	srand(time(0));
	cin>>n;
	if(n==2){
		road[1][0]=road[0][1]=1;
		outprint();
	}
	while(1){
	road[0][1]=road[1][0]=1,road[1][2]=road[2][1]=2,road[0][2]=road[2][0]=3;
	for(int i=3;i<n;i++){
		solve(i);
		random_shuffle(rati,rati+i);
		for(int j=0;j<i;j++){
			road[j][i]=road[i][j]=(M)*rati[j];
		}
	}
	solve(n);
	if(M<1e11) 
	outprint();
}
	
	return 0;
}