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 PYTHON3):

Solution:
import sys
input = sys.stdin.readline

import itertools

N = int(input())

A = [1,2,4]
for _ in range(12):
    sum_2 = set(x+y for x,y in itertools.combinations(A,2))
    avoid = set(x-y for x,y in itertools.product(sum_2,A))
    x = min(set(range(1,1000)) - avoid - sum_2 - set(A))
    A.append(x)

L = [[0] * (N-1-i) for i in range(N)]

x = 1
for n in range(N):
    L[n] = [x*a for a in A[:N-1-n]]
    if n < N-2:
        x = L[n][-1] + L[n][-2]

graph = [[0] * N for _ in range(N)]
for i in range(N):
    for j,x in enumerate(L[i]):
        graph[i][i+j+1] = x
        graph[i+j+1][i] = x

for row in graph:
    print(*row)