Problem: Let's call some square matrix with integer values in its cells palindromic if it doesn't change after the order of rows is reversed and it doesn't change after the order of columns is reversed.

For example, the following matrices are palindromic:

<image>

The following matrices are not palindromic because they change after the order of rows is reversed:

<image>

The following matrices are not palindromic because they change after the order of columns is reversed:

<image>

You are given n^2 integers. Put them into a matrix of n rows and n columns so that each number is used exactly once, each cell contains exactly one number and the resulting matrix is palindromic. If there are multiple answers, print any. If there is no solution, print "NO".

Input

The first line contains one integer n (1 ≤ n ≤ 20).

The second line contains n^2 integers a_1, a_2, ..., a_{n^2} (1 ≤ a_i ≤ 1000) — the numbers to put into a matrix of n rows and n columns.

Output

If it is possible to put all of the n^2 numbers into a matrix of n rows and n columns so that each number is used exactly once, each cell contains exactly one number and the resulting matrix is palindromic, then print "YES". Then print n lines with n space-separated numbers — the resulting matrix.

If it's impossible to construct any matrix, then print "NO".

You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.

Examples

Input


4
1 8 8 1 2 2 2 2 2 2 2 2 1 8 8 1


Output


YES
1 2 2 1
8 2 2 8
8 2 2 8
1 2 2 1


Input


3
1 1 1 1 1 3 3 3 3


Output


YES
1 3 1
3 1 3
1 3 1


Input


4
1 2 1 9 8 4 3 8 8 3 4 8 9 2 1 1


Output


NO


Input


1
10


Output


YES
10 

Note

Note that there exist multiple answers for the first two examples.

Solution (in PYTHON3):

Solution:
def is_palindromic(lst, n):

	
	#check how many different numbers could be in the n-matrix
	len_set = len(set(lst))
	set_ = set(lst)
	
	if n%2 == 0:
		a = n*n/4
	else:
		a = (n+1)*(n+1)/4

	if len_set > a:
		print("NO")
		return

	if len(lst) != n*n:
		print("no")
		return

	#dictionary with a number of different numbers
	dict_ = {}
	for i in lst:
		if i not in dict_:
			dict_[i] = 1
		else:
			dict_[i] += 1

	#check if the number of different numbers are ok for the n-matrix

	#n=1, always ok, print and return
	if n == 1:
		print('YES')
		# print(' '.join(map(str, lst)))
		matrix = print_matrix(dict_, n)
		return matrix

	# n=2, ok only when all numbers the same, we check it before(len set)
	elif n == 2:
		print("YES")
		for i in range(n):
			# print(' '.join(map(str, lst[i:i+2])))
			matrix = print_matrix(dict_, n)
			return matrix

	# n: even numbers, not 2
	elif n%2 == 0 and n != 2:
		for key, value in enumerate(dict_.items()):
			if value[1] % 4 != 0:
				print("NO")
				return
		else:
			print("yes")
			matrix = print_matrix(dict_, n)
			return matrix

	elif n%2 != 0:
		ksi = n-1
		psi = 0
		for key, value in enumerate(dict_.items()):
			if value[1] % 4 != 0 and value[1] % 2 == 0:
				psi += 1
		if psi>ksi:
			print("NO")
			return

		else:
			odd = 0
			two = 0
			for key, value in enumerate(dict_.items()):
				if value[1] % 2 != 0:
					odd += 1
					if odd > 1:
						print("NO")
						return
				elif value[1] == 2:
					two += 1
					if two > n-1:
						print("no")
						return
			else:
				print("yes")
				matrix = print_matrix(dict_, n)
				return matrix

def print_matrix(dict_, n):
	
	Matrix = [[0 for x in range(n)] for y in range(n)] 

	lst_2 = []
	lst_2_2 = []
	lst_2_2_2 = []
	lst_4 = []
	odd_num = 0
	pairs_without_quarters = 0

	for key, value in enumerate(dict_.items()):

		if value[1] % 2 == 0 and value[1] % 4 != 0:
			lst_2.append(value[0])
			pairs_without_quarters += 1

		elif value[1] % 4 == 0:
			lst_4.append(value[0])
			
		else:
			odd_num += value[0]

	if n%2 != 0:
		odd_num_num = dict_[odd_num]

		if odd_num != 0:
			Matrix[n//2][n//2] = odd_num
			dict_[odd_num] -= 1

		if dict_[odd_num] == 0:
			odd_num = 0
		elif dict_[odd_num]%4 != 0:
			Matrix[n//2][(n//2)-1] = odd_num
			Matrix[n//2][(n//2)+1] = odd_num
	
			if dict_[odd_num] == 2:
				odd_num = 0
			else:
				dict_[odd_num] -= 2

		if len(lst_2) != 0:
			if len(lst_2) >= n//2:
				for i in range(n//2):
					Matrix[i][n//2] = lst_2[i]
					Matrix[n-1-i][n//2] = lst_2[i]
					dict_[lst_2[i]] -= 2

					if dict_[lst_2[i]] == 0:
						lst_2[i] = 0

			else:
				for i in range(len(lst_2)):
					Matrix[i][n//2] = lst_2[i]
					Matrix[n-1-i][n//2] = lst_2[i]
					dict_[lst_2[i]] -= 2

			for item in lst_2:

				if item > 0 and dict_[item] % 4 == 0:
					lst_4.append(item)
				elif item > 0:
					lst_2_2.append(item)

		if len(lst_2_2) != 0:

			if len(lst_2_2) >= n//2:
				for j in range(n//2):
					Matrix[n//2][j] = lst_2_2[j]
					Matrix[n//2][n-1-j] = lst_2_2[j]
					dict_[lst_2_2[j]] -= 2

					if dict_[lst_2_2[j]] == 0:
						lst_2_2[j] = 0
					
			else:
				for j in range(len(lst_2_2)):
					Matrix[n//2][j] = lst_2_2[j]
					Matrix[n//2][n-1-j] = lst_2_2[j]
					dict_[lst_2_2[j]] -= 2

			for item in lst_2_2:

				if item > 0 and dict_[item] % 4 == 0:
					lst_4.append(item)
				elif item > 0:
					lst_2_2_2.append(item)

	for i in range(n):
		
		if len(lst_4) == 0 and odd_num == 0:
				break
		for j in range(n//2+1):

			if len(lst_4) == 0 and odd_num == 0:
				break
			
			if Matrix[i][j] == 0 and len(lst_4) != 0 and n%2 == 0:

				z = dict_[lst_4[0]]//4

				ii = i
				jj = j
	
			
				while z:
					
					if Matrix[i][j] == 0:
						Matrix[i][j] = lst_4[0]
						Matrix[i][n-j-1] = lst_4[0]
						Matrix[n-i-1][j] = lst_4[0]
						Matrix[n-i-1][n-j-1] = lst_4[0]
						z -= 1
				
					if j == (n-1)//2:
						i += 1
						j = 0
						
					else:
						j += 1
				
				del lst_4[0]

				i = ii
				j = jj

			elif Matrix[i][j] == 0 and len(lst_4) != 0:

				b = dict_[lst_4[0]]
	
				z = b//4
				
				ii = i
				jj = j
		
				while z:

					
					if Matrix[i][j] == 0 and i != (n-1)//2 and j != (n-1)//2:

						Matrix[i][j] = lst_4[0]
						Matrix[i][n-1-j]= lst_4[0]
						Matrix[n-i-1][j] = lst_4[0]
						Matrix[n-i-1][n-1-j] = lst_4[0]
						z -= 1

					elif Matrix[i][j] == 0 and j == (n-1)//2 and i != ((n-1)//2)-1:

						Matrix[i][j] = lst_4[0]
						Matrix[i+1][j] = lst_4[0]
						Matrix[n-i-1][j] = lst_4[0]
						Matrix[n-i-2][j] = lst_4[0]
						z -= 1

					elif Matrix[i][j] == 0 and i == (n-1)//2:

						Matrix[i][j] = lst_4[0]
						Matrix[i][n-j-1] = lst_4[0]
						if j+1 != n-j-2:
							Matrix[i][j+1]= lst_4[0]
							Matrix[i][n-j-2] = lst_4[0]
							j += 1
						else:
							Matrix[i-1][n//2]= lst_4[0]
							Matrix[i+1][n//2] = lst_4[0]

						z -= 1
						
					
					if j == ((n-1)//2):
						
						i += 1
						j = 0
					else:
						j += 1

				i = ii
				j = jj
					
				del lst_4[0]

			elif Matrix[i][j] == 0 and odd_num != 0:

				b = dict_[odd_num]
				k = 0
				i = 0
				j = 0

				while b:
					
					if Matrix[i][j] == 0:
						Matrix[i][j] = odd_num
						b -= 1

					if j == (n-1):
						i += 1
						j = 0
					else:
						j += 1

				odd_num = 0
				
							
	for rows in Matrix:
		rows = str(rows).replace(", ", " ")
		rows = rows.strip("]")
		rows = rows.strip("[")
		print(rows)

n = int(input())
lst = list(map(int, input().split()))
is_palindromic(lst, n)