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>
long long s[][11]={{0,1,2,7,45,512,9925,321381,15870550,1069877351,},{1,0,4,14,90,1024,19850,642762,31741100,2139754702,},{2,4,0,28,180,2048,39700,1285524,63482200,4279509404,},{7,14,28,0,315,3584,69475,2249667,111093850,7489141457,},{45,90,180,315,0,6144,119100,3856572,190446600,12838528212,},{512,1024,2048,3584,6144,0,198500,6427620,317411000,21397547020,},{9925,19850,39700,69475,119100,198500,0,9320049,460245950,31026443179,},{321381,642762,1285524,2249667,3856572,6427620,9320049,0,603080900,40655339338,},{15870550,31741100,63482200,111093850,190446600,317411000,460245950,603080900,0,55633622252,},{1069877351,2139754702,4279509404,7489141457,12838528212,21397547020,31026443179,40655339338,55633622252,0,}};
int main(){
	int n;scanf("%d",&n);
	for(int i=0;i<n;++i){for(int j=0;j<n;++j)printf("%lld ",s[i][j]);puts("");}
	return 0;
}