Problem: We will consider the numbers a and b as adjacent if they differ by exactly one, that is, |a-b|=1.

We will consider cells of a square matrix n × n as adjacent if they have a common side, that is, for cell (r, c) cells (r, c-1), (r, c+1), (r-1, c) and (r+1, c) are adjacent to it.

For a given number n, construct a square matrix n × n such that: 

  * Each integer from 1 to n^2 occurs in this matrix exactly once; 
  * If (r_1, c_1) and (r_2, c_2) are adjacent cells, then the numbers written in them must not be adjacent. 

Input

The first line contains one integer t (1 ≤ t ≤ 100). Then t test cases follow.

Each test case is characterized by one integer n (1 ≤ n ≤ 100).

Output

For each test case, output: 

  * -1, if the required matrix does not exist; 
  * the required matrix, otherwise (any such matrix if many of them exist). 



The matrix should be outputted as n lines, where each line contains n integers.

Example

Input


3
1
2
3


Output


1
-1
2 9 7
4 6 3
1 8 5

Solution (in PYTHON3):

Solution:
import sys,os
from io import BytesIO,IOBase
mod = 10**9+7; Mod = 998244353; INF = float('inf')
# input = lambda: sys.stdin.readline().rstrip("\r\n")
# inp = lambda: list(map(int,sys.stdin.readline().rstrip("\r\n").split()))
#______________________________________________________________________________________________________
# region fastio
# ''' 
BUFSIZE = 8192
class FastIO(IOBase):
    newlines = 0
    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
# endregion'''
#______________________________________________________________________________________________________
input = lambda: sys.stdin.readline().rstrip("\r\n")
inp = lambda: list(map(int,sys.stdin.readline().rstrip("\r\n").split()))
# ______________________________________________________________________________________________________
# from math import *
# from bisect import *
# from heapq import *
# from collections import defaultdict as dd
# from collections import OrderedDict as odict
# from collections import Counter as cc
# from collections import deque
# from itertools import groupby
# sys.setrecursionlimit(200400) #this is must for dfs
# ______________________________________________________________________________________________________
# segment tree for range minimum query and update 0 indexing
# init = float('inf')
# st = [init for i in range(4*len(a))]
# def build(a,ind,start,end):
#     if start == end:
#         st[ind] = a[start]
#     else:
#         mid = (start+end)//2
#         build(a,2*ind+1,start,mid)
#         build(a,2*ind+2,mid+1,end)
#         st[ind] = min(st[2*ind+1],st[2*ind+2])
# build(a,0,0,n-1)
# def query(ind,l,r,start,end):
#     if start>r or end<l:
#         return init
#     if l<=start<=end<=r:
#         return st[ind]
#     mid = (start+end)//2
#     return min(query(2*ind+1,l,r,start,mid),query(2*ind+2,l,r,mid+1,end))
# def update(ind,val,stind,start,end):
# 	if start<=ind<=end:
# 		if start==end:
# 			st[stind] = a[start] = val
# 		else:
# 			mid = (start+end)//2
# 			update(ind,val,2*stind+1,start,mid)
# 			update(ind,val,2*stind+2,mid+1,end)
# 			st[stind] = min(st[left],st[right])
# ______________________________________________________________________________________________________
# Checking prime in O(root(N))
# def isprime(n):
#     if (n % 2 == 0 and n > 2) or n == 1: return 0
#     else:
#         s = int(n**(0.5)) + 1
#         for i in range(3, s, 2):
#             if n % i == 0:
#                 return 0
#         return 1
# def lcm(a,b):
#   return (a*b)//gcd(a,b)
# ______________________________________________________________________________________________________
# nCr under mod
# def C(n,r,mod = 10**9+7):
#   if r>n: return 0
#   if r>n-r: r = n-r
#   num = den = 1
#   for i in range(r):
#       num = (num*(n-i))%mod
#       den = (den*(i+1))%mod
#   return (num*pow(den,mod-2,mod))%mod
# def C(n,r):
#   if r>n:
#       return 0
#   if r>n-r:
#       r = n-r
#   ans = 1
#   for i in range(r):
#       ans = (ans*(n-i))//(i+1)
#   return ans
# ______________________________________________________________________________________________________
# For smallest prime factor of a number
# M = 2*10**5+10
# spf = [i for i in range(M)]
# def spfs(M):
#   for i in range(2,M):
#       if spf[i]==i:
#           for j in range(i*i,M,i):
#               if spf[j]==j:
#                 spf[j] = i
#   return
# spfs(M)
# ______________________________________________________________________________________________________
# def gtc(p):
#     print('Case #'+str(p)+': ',end='')
# ______________________________________________________________________________________________________
tc = 1
tc = int(input())
for test in range(1,tc+1):
    n = int(input())
    if n==2:
        print(-1)
        continue
    a = [[0]*n for i in range(n)]
    cnt = 1
    for i in range(n):
        a[i][i] = cnt
        cnt+=1
    cnt1 = cnt
    cnt2 = cnt+1
    for i in range(n):
        for j in range(n):
            if i<j:
                a[i][j] = cnt1
                cnt1+=2
            if j<i:
                a[i][j] = cnt2
                cnt2+=2
    for i in a:
        print(*i)