Problem:


Score : 1100 points

Problem Statement

You are given an integer N.

Construct any one N-by-N matrix a that satisfies the conditions below. It can be proved that a solution always exists under the constraints of this problem.

1 \leq a_{i,j} \leq 10^{15}

a_{i,j} are pairwise distinct integers.

There exists a positive integer m such that the following holds: Let x and y be two elements of the matrix that are vertically or horizontally adjacent. Then, {\rm max}(x,y) {\rm mod} {\rm min}(x,y) is always m.

Constraints

2 \leq N \leq 500

Input

Input is given from Standard Input in the following format:

N

Output

Print your solution in the following format:

a_{1,1} ... a_{1,N}
:
a_{N,1} ... a_{N,N}

Sample Input 1

2

Sample Output 1

4 7
23 10

For any two elements x and y that are vertically or horizontally adjacent, {\rm max}(x,y) {\rm mod} {\rm min}(x,y) is always 3.



Sample input:
2


Sample output:
4 7
23 10

Submission status: Wrong Answer

Solution code:
import numpy as np
import math
from functools import reduce

def lcm_base(x,y):
    return (x*y) // math.gcd(x,y)

def koubaisuu(i,j):
    lst = [arr[i-1][j],arr[i+1][j],arr[i][j-1],arr[i][j+1]]
    return reduce(lcm_base,lst,1)

N = int(input())
if N == 2:
    print(4,7)
    print(23,10)
    exit()
arr = np.array([[0] * (N+2) for _ in range(N+2)])
arr[0,:],arr[:,0],arr[-1,:],arr[:,-1] = 1,1,1,1

nums_lst = list(range(2, N ** 2 // 2 + 3))
#print(nums_lst)

for i in range(1,N+1):
    for j in range(1,N+1,2):
        if i % 2 != 0:
            arr[i][j] = nums_lst.pop(0)
        else:
            if j != N:
                arr[i][j+1] = nums_lst.pop(-1)
            else:
                break
            
for i in range(len(arr)):
    for j in range(len(arr)):
        if arr[i][j] == 0:
            arr[i][j] = koubaisuu(i,j) + 1
        
a = np.delete(arr,[0],1)
b = np.delete(a,np.s_[-1],1)
c = np.delete(b,[0],0)
d = np.delete(c,np.s_[-1],0)

for i in d:
    print(*i)

Submission status: Wrong Answer

Solution code:
import numpy as np
import math
from functools import reduce

def lcm_base(x,y):
    return (x*y) // math.gcd(x,y)

def koubaisuu(i,j):
    lst = [arr[i-1][j],arr[i+1][j],arr[i][j-1],arr[i][j+1]]
    return reduce(lcm_base,lst,1)

N = int(input())
arr = np.array([[0] * (N+2) for _ in range(N+2)])
arr[0,:],arr[:,0],arr[-1,:],arr[:,-1] = 1,1,1,1

nums_lst = list(range(2, N ** 2 // 2 + 3))
#print(nums_lst)

for i in range(1,N+1):
    for j in range(1,N+1,2):
        if i % 2 != 0:
            arr[i][j] = nums_lst.pop(0)
        else:
            if j != N:
                arr[i][j+1] = nums_lst.pop(-1)
            else:
                break
            
for i in range(len(arr)):
    for j in range(len(arr)):
        if arr[i][j] == 0:
            arr[i][j] = koubaisuu(i,j) + 1
        
a = np.delete(arr,[0],1)
b = np.delete(a,np.s_[-1],1)
c = np.delete(b,[0],0)
d = np.delete(c,np.s_[-1],0)

for i in d:
    print(*i)

Submission status: Wrong Answer

Solution code:
from math import gcd
Primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973]
N = int(input())
a = []
for i in range(N):
  a.append([])
  for j in range(N):
    if (i + j) % 2 == 0:
      a[i].append(Primes[250 + (i - j) // 2] * Primes[500 + (i + j) // 2])
    else:
      a[i].append(0)

for i in range(N):
  for j in range(N):
    if (i + j) % 2 != 0:
      mul = 1
      if i > 0:
        mul = mul * a[i-1][j] // gcd(mul,a[i-1][j])
      if j > 0:
        mul = mul * a[i][j-1] // gcd(mul,a[i][j-1])
      if i < N-1:
        mul = mul * a[i+1][j] // gcd(mul,a[i+1][j])
      if j < N - 1:
        mul = mul * a[i][j+1] // gcd(mul,a[i][j+1])
      mul += 1
      a[i][j] = mul

for row in a:
  print(" ".join(map(str,row)))

Submission status: Wrong Answer

Solution code:
N = int(input())
 
a = []
for i in range(N + 2):
  a.append([0] * (N + 2))
cur = 101
for i in range(N + 2):
  for j in range(N + 2):
    if (i + j) % 2 == 0:
      a[i][j] = cur
      cur += 1

for i in range(N + 2):
  for j in range(N + 2):
    if (i + j) % 2 != 0:
      mul = 1
      if i > 0:
        mul *= a[i-1][j]
      if j > 0:
        mul *= a[i][j-1]
      if i < N + 1:
        mul *= a[i+1][j]
      if j < N + 1:
        mul *= a[i][j+1]
      a[i][j] = mul + 1
 
      
for aList in a[1:-1]:
  print(" ".join(map(str,aList[1:-1])))

Submission status: Wrong Answer

Solution code:
N = int(input())

a = []
for i in range(N):
  a.append([0] * N)
cur = 10001
for i in range(N):
  for j in range(N):
    if (i + j) % 2 == 0:
      a[i][j] = cur
      cur += 1

for i in range(N):
  for j in range(N):
    if (i + j) % 2 != 0:
      mul = 1
      if i > 0:
        mul *= a[i-1][j]
      if j > 0:
        mul *= a[i][j-1]
      if i < N - 1:
        mul *= a[i+1][j]
      if j < N - 1:
        mul *= a[i][j+1]
      a[i][j] = mul + 1

for aList in a:
  print(" ".join(map(str,aList)))

Submission status: Wrong Answer

Solution code:
N = int(input())

a = []
for i in range(N):
  a.append([0] * N)
cur = 101
for i in range(N):
  for j in range(N):
    if (i + j) % 2 == 0:
      a[i][j] = cur
      cur += 1

for i in range(N):
  for j in range(N):
    if (i + j) % 2 != 0:
      mul = 1
      if i > 0:
        mul *= a[i-1][j]
      if j > 0:
        mul *= a[i][j-1]
      if i < N - 1:
        mul *= a[i+1][j]
      if j < N - 1:
        mul *= a[i][j+1]
      a[i][j] = mul + 1

for aList in a:
  print(" ".join(map(str,aList)))

Submission status: Wrong Answer

Solution code:
N=int(input())
for i in range(N):
  L=list(range(i+2,i+2+N))
  L=list(map(str,L))
  print(" ".join(L))

Submission status: Wrong Answer

Solution code:
N = int(input())

n_1 = N % 2
n_2 = N // 2

PN = [2]
L = 3
while len(PN) < N*2:
    c = True
    for p in PN:
        if L % p == 0: c = False
    if c == True: PN.append(L)
    L += 2

a = [[1]*N for _ in range(N)]
b = [[1]*N for _ in range(N)]

if n_1 == 1:
    w = 1
    for i in range(n_2):
        if w > 0:
            for j in range(i+1):
                a[i + j][i - j] = PN[4*i]
                a[i - j][i + j] = PN[4*i]
                a[N-1-i + j][N-1-i - j] = PN[4*i+1]
                a[N-1-i - j][N-1-i + j] = PN[4*i+1]
                b[i + j][N-1-i + j] = PN[4*i+2]
                b[i - j][N-1-i - j] = PN[4*i+2]
                b[N-1-i + j][i + j] = PN[4*i+3]
                b[N-1-i - j][i - j] = PN[4*i+3]
        else:
            for j in range(i+1):
                a[i + j][i - j] = PN[-4*(i-1)-1]
                a[i - j][i + j] = PN[-4*(i-1)-1]
                a[N-1-i + j][N-1-i - j] = PN[-4*(i-1)-2]
                a[N-1-i - j][N-1-i + j] = PN[-4*(i-1)-2]
                b[i + j][N-1-i + j] = PN[-4*(i-1)-3]
                b[i - j][N-1-i - j] = PN[-4*(i-1)-3]
                b[N-1-i + j][i + j] = PN[-4*(i-1)-4]
                b[N-1-i - j][i - j] = PN[-4*(i-1)-4]
        w *= -1
    r = (n_2-1)//2+1
    for j in range(n_2+1):
        a[n_2 + j][n_2 - j] = PN[4*r]
        a[n_2 - j][n_2 + j] = PN[4*r]
        b[n_2 + j][n_2 + j] = PN[4*r+1]
        b[n_2 - j][n_2 - j] = PN[4*r+1]
else:
    w = 1
    for i in range(n_2):
        if w > 0:
            for j in range(i+1):
                a[i + j][i - j] = PN[4*i]
                a[i - j][i + j] = PN[4*i]
                a[N-1-i + j][N-1-i - j] = PN[4*i+1]
                a[N-1-i - j][N-1-i + j] = PN[4*i+1]
                b[i+1 + j][N-1-i + j] = PN[4*i+3]
                b[i - j][N-2-i - j] = PN[4*i+3]
                b[N-1-i + j][i+1 + j] = PN[4*i+2]
                b[N-2-i - j][i - j] = PN[4*i+2]
        else:
            for j in range(i+1):
                a[i + j][i - j] = PN[-4*(i-1)-1]
                a[i - j][i + j] = PN[-4*(i-1)-1]
                a[N-1-i + j][N-1-i - j] = PN[-4*(i-1)-2]
                a[N-1-i - j][N-1-i + j] = PN[-4*(i-1)-2]
                b[i+1 + j][N-1-i + j] = PN[-4*(i-1)-4]
                b[i - j][N-2-i - j] = PN[-4*(i-1)-4]
                b[N-1-i + j][i+1 + j] = PN[-4*(i-1)-3]
                b[N-2-i - j][i - j] = PN[-4*(i-1)-3]
        w *= -1

c = [[1]*N for _ in range(N)]
for i in range(N):
    for j in range(N):
        c[i][j] = a[i][j] * b[i][j]

if n_1 == 1:
    for i in range(n_2+1):
        for j in range(n_2):
            c[2*i][1+2*j] += c[2*i][1+2*j - 1] * c[2*i][1+2*j + 1]
    for i in range(n_2):
        for j in range(n_2+1):
            c[1+2*i][2*j] += c[1+2*i - 1][2*j] * c[1+2*i + 1][2*j]
else:
    for i in range(n_2-1):
        for j in range(n_2):
            c[1+2*i][2*j] += c[1+2*i - 1][2*j] * c[1+2*i + 1][2*j]
            c[1+2*i + 1][2*j + 1] += c[1+2*i - 1 + 1][2*j + 1] * c[1+2*i + 1 + 1][2*j + 1]
    for j in range(n_2-1):
        c[0][1+2*j] += c[0][1+2*j - 1] * c[0][1+2*j + 1]
        c[-1][2+2*j] += c[-1][2+2*j - 1] * c[-1][2+2*j + 1]
    c[0][-1] += a[0][-2] * a[1][-1] * b[0][-2]
    c[-1][0] += a[-2][0] * a[-1][1] * b[-1][1] * 2

for C in c:
    print(*C)

Submission status: Wrong Answer

Solution code:
N = int(input())

n_1 = N % 2
n_2 = N // 2

PN = [2]
L = 3
while len(PN) < N*2:
    c = True
    for p in PN:
        if L % p == 0: c = False
    if c == True: PN.append(L)
    L += 2

a = [[1]*N for _ in range(N)]
b = [[1]*N for _ in range(N)]

if n_1 == 1:
    w = 1
    for i in range(n_2):
        if w > 0:
            for j in range(i+1):
                a[i + j][i - j] = PN[4*i]
                a[i - j][i + j] = PN[4*i]
                a[N-1-i + j][N-1-i - j] = PN[4*i+1]
                a[N-1-i - j][N-1-i + j] = PN[4*i+1]
                b[i + j][N-1-i + j] = PN[4*i+2]
                b[i - j][N-1-i - j] = PN[4*i+2]
                b[N-1-i + j][i + j] = PN[4*i+3]
                b[N-1-i - j][i - j] = PN[4*i+3]
        else:
            for j in range(i+1):
                a[i + j][i - j] = PN[-4*(i-1)-1]
                a[i - j][i + j] = PN[-4*(i-1)-1]
                a[N-1-i + j][N-1-i - j] = PN[-4*(i-1)-2]
                a[N-1-i - j][N-1-i + j] = PN[-4*(i-1)-2]
                b[i + j][N-1-i + j] = PN[-4*(i-1)-3]
                b[i - j][N-1-i - j] = PN[-4*(i-1)-3]
                b[N-1-i + j][i + j] = PN[-4*(i-1)-4]
                b[N-1-i - j][i - j] = PN[-4*(i-1)-4]
        w *= -1
    r = (n_2-1)//2+1
    for j in range(n_2+1):
        a[n_2 + j][n_2 - j] = PN[4*r]
        a[n_2 - j][n_2 + j] = PN[4*r]
        b[n_2 + j][n_2 + j] = PN[4*r+1]
        b[n_2 - j][n_2 - j] = PN[4*r+1]
else:
    w = 1
    for i in range(n_2):
        if w > 0:
            for j in range(i+1):
                a[i + j][i - j] = PN[4*i]
                a[i - j][i + j] = PN[4*i]
                a[N-1-i + j][N-1-i - j] = PN[4*i+1]
                a[N-1-i - j][N-1-i + j] = PN[4*i+1]
                b[i+1 + j][N-1-i + j] = PN[4*i+3]
                b[i - j][N-2-i - j] = PN[4*i+3]
                b[N-1-i + j][i+1 + j] = PN[4*i+2]
                b[N-2-i - j][i - j] = PN[4*i+2]
        else:
            for j in range(i+1):
                a[i + j][i - j] = PN[-4*(i-1)-1]
                a[i - j][i + j] = PN[-4*(i-1)-1]
                a[N-1-i + j][N-1-i - j] = PN[-4*(i-1)-2]
                a[N-1-i - j][N-1-i + j] = PN[-4*(i-1)-2]
                b[i+1 + j][N-1-i + j] = PN[-4*(i-1)-4]
                b[i - j][N-2-i - j] = PN[-4*(i-1)-4]
                b[N-1-i + j][i+1 + j] = PN[-4*(i-1)-3]
                b[N-2-i - j][i - j] = PN[-4*(i-1)-3]
        w *= -1

c = [[1]*N for _ in range(N)]
for i in range(N):
    for j in range(N):
        c[i][j] = a[i][j] * b[i][j]

if n_1 == 1:
    for i in range(n_2+1):
        for j in range(n_2):
            c[2*i][1+2*j] += c[2*i][1+2*j - 1] * c[2*i][1+2*j + 1]
    for i in range(n_2):
        for j in range(n_2+1):
            c[1+2*i][2*j] += c[1+2*i - 1][2*j] * c[1+2*i + 1][2*j]
else:
    for i in range(n_2-1):
        for j in range(n_2):
            c[1+2*i][2*j] += c[1+2*i - 1][2*j] * c[1+2*i + 1][2*j]
            c[1+2*i + 1][2*j + 1] += c[1+2*i - 1 + 1][2*j + 1] * c[1+2*i + 1 + 1][2*j + 1]
    for j in range(n_2-1):
        c[0][1+2*j] += c[0][1+2*j - 1] * c[0][1+2*j + 1]
        c[-1][2+2*j] += c[-1][2+2*j - 1] * c[-1][2+2*j + 1]
    c[0][-1] += a[0][-2] * a[1][-1] * b[0][-2]
    c[-1][0] += a[-2][0] * a[-1][1] * b[-1][1] * 2

print(PN)
for C in c:
    print(*C)

Submission status: Wrong Answer

Solution code:
import fractions
import sys

def lcm(a,b):
    return a * b // fractions.gcd(a,b)

N = int(input())

if N == 2:
    print ("4 7")
    print ("23 10")
    sys.exit()

lis = [2]

now = 3
while len(lis) < 2 * N:

    flag = True
    for i in lis:
        if now % i == 0:
            flag = False
            break

    if flag:
        lis.append(now)
    now += 2

#print (lis)

ans = [ [1] * N for i in range(N) ]


for loop in range(2 * N):

    if loop % 2 == 0:

        i = loop
        j = 0

        while i >= 0:
            if i < N and j < N:
                ans[i][j] *= lis[loop // 2]

            i -= 1
            j += 1



m = -1
for loop in range(2 * N):

    if (N - 1 - loop) % 2 == 0:

        i = 0
        j = N-1-loop

        while i < N and (i + j) % 2 == 0:
            if i < N and j < N:
                ans[i][j] *= lis[m]

            i += 1
            j += 1
            
        m -= 1



for i in range(N):
    for j in range(N):

        if (i + j) % 2 == 1:

            t = 1

            if i > 0:
                t = lcm(t,ans[i-1][j])
            
            if j > 0:
                t = lcm(t,ans[i][j-1])
            

            if i < N-1:
                t = lcm(t,ans[i+1][j])
            

            if j < N-1:
                t = lcm(t,ans[i][j+1])

            ans[i][j] = t+1
            

for i in range(N):
    print (" ".join(map(str,ans[i])))

Submission status: Wrong Answer

Solution code:
N = int(input())
xzero = 3
yzero = 5
y = N+1

biggest = 8*(int(N/4)+1)*(int(N/4)+1)+4
a = [[0 for i in range(N+4)] for j in range(N+4)]
fours = [4*i for i in range((int(N/4)+1))]
odds = [2*i for i in range(int((N+1)/2))]
evens = [2*i+1 for i in range(int(N/2))]

if N==2:
    print("4 7")
    print("23 10")
else:
    x = xzero
    for i in fours:
        for j in fours:
            a[i][j] = x
            a[i+1][j+1] = 2*x
            a[i][j+2]=biggest-x
            a[i+1][j+3] = 2*(biggest-x)
            a[i+2][j] = biggest-x-(int(N/4)+1)*2
            a[i+3][j+1] = 2*(biggest-x-(int(N/4)+1)*2)
            a[i+2][j+2] = x+(int(N/4)+1)*2
            a[i+3][j+3] = 2*(x+(int(N/4)+1)*2)
            x += 2
        x+=(int(N/4)+1)*2

    for i in odds:
        for j in evens:
            ans = 1
            ans *= a[i][j - 1]
            ans *= a[i][j + 1]
            if i > 0:
                ans *= a[i - 1][j]
            else:
                ans *= 2
            ans += 1
            a[i][j] = ans

    for i in evens:
        for j in odds:
            ans = 1
            ans *= a[i - 1][j]
            ans *= a[i + 1][j]
            if j > 0:
                ans *= a[i][j - 1]
            else:
                ans *= 2
            ans += 1
            a[i][j] = ans
    print(a)
    a = [i[0:N] for i in a[0:N]]

    for i in range(N):
        print(" ".join(str(j) for j in a[i]))

Submission status: Wrong Answer

Solution code:
N = int(input())
x = N
y = N+1
a = [[0 for i in range(N)] for j in range(N)]
odds = [2*i for i in range(int((N+1)/2))]
evens = [2*i+1 for i in range(int(N/2))]

if N==2:
    print("4 7")
    print("23 10")
else:
    for i in odds:
        for j in odds:
            a[i][j] = x
            x += 2
    for i in evens:
        for j in evens:
            a[i][j] = y
            y += 2

    for i in odds:
        for j in evens:
            ans = 1
            ans *= a[i][j - 1]
            if j < N - 1:
                ans *= a[i][j + 1]
            if i > 0:
                ans *= a[i - 1][j]
            if i < N - 1:
                ans *= a[i + 1][j]
            ans += 1
            a[i][j] = ans

    for i in evens:
        for j in odds:
            ans = 1
            ans *= a[i - 1][j]
            if i < N - 1:
                ans *= a[i + 1][j]
            if j > 0:
                ans *= a[i][j - 1]
            if j < N - 1:
                ans *= a[i][j + 1]
            ans += 1
            a[i][j] = ans

    for i in range(N):
        print(" ".join(str(j) for j in a[i]))

Submission status: Wrong Answer

Solution code:
N = int(input())
a= [[0] * N for _ in range(N)]

if N == 2:
    print(4, 7)
    print(23, 10)
    exit()

def sieve(n):
    '''
    :param n:
    :return: n以下の素数のリストを返す
    エラトステネスの篩→O(n log log n)
    '''
    prime = []
    is_prime = [True] * (n + 1) #is_prime[i] = Trueならiは素数
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, n+1):
        if is_prime[i]:
            prime.append(i)
            for j in range(2 * i, n + 1, i):
                is_prime[j] = False
    return prime

P = sieve(8 * (10 ** 5))
for i in range((N + 1) // 2):
    for j in range((N + 1) // 2):
        a[2 * i][2 * j] = P[i * ((N + 1) // 2) + j + 1]

for i in range(N // 2):
    for j in range(N // 2):
        a[2 * i + 1][2 * j + 1] = P[-(i * (N // 2) + j + 1)]


def prod_around(x, y):
    #a[x][y]の周囲のマスの積 + 1 を返す
    ans = 1
    diff = [(1, 0), (-1, 0), (0, 1), (0, -1)]
    for d in diff:
        i, j = d
        if 0 <= x + i < N and 0 <= y + j < N:
            ans *= a[x + i][y + j]
    ans += 1
    return ans

for i in range((N + 1) // 2):
    for j in range(N // 2):
        a[2 * i][2 * j + 1] = prod_around(2 * i, 2 * j + 1)
        a[2 * j + 1][2 * i] = prod_around(2 * j + 1, 2 * i)

for i in range(N):
    print(' '.join(map(str, a[i])))

Submission status: Wrong Answer

Solution code:
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
def inpl(): return list(map(int, input().split()))
def inpls(): return list(input().split())

N = int(input())

#最大公約数
def gcd(a,b):
	while b:
		a,b = b, a%b
	return a

#最小公倍数
def lcm(a,b):
	return a*b // gcd(a,b)

ans = [[0]*N for i in range(N)]

tmp = 2
for y in range(N):
	if y%2 == 0:
		xx = range(0,N,2)
	else:
		xx = range(1,N,2)

	for x in xx:
		pl = y+x+1
		mn = y-x + N*2 + N%2+1
		ans[y][x] = pl*mn

ed = defaultdict(bool)
for y in range(N):
    for x in range(N):
        if ans[y][x] == 0:
            tmp = 1
            if x > 0:
                tmp = lcm(tmp,ans[y][x-1])
            if x < N-1:
                tmp = lcm(tmp,ans[y][x+1])
            if y > 0:
                tmp = lcm(tmp,ans[y-1][x])
            if y < N-1:
                tmp = lcm(tmp,ans[y+1][x])

            while ed[tmp+1]:
                tmp += tmp

            ans[y][x] = tmp + 1
            ed[tmp+1] = True


for a in ans:
    print(' '.join(map(str,a)))

Submission status: Wrong Answer

Solution code:
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
def inpl(): return list(map(int, input().split()))
def inpls(): return list(input().split())

N = int(input())

#最大公約数
def gcd(a,b):
	while b:
		a,b = b, a%b
	return a

#最小公倍数
def lcm(a,b):
	return a*b // gcd(a,b)

ans = [[0]*N for i in range(N)]

tmp = 2
for y in range(N):
	if y%2 == 0:
		xx = range(0,N,2)
	else:
		xx = range(1,N,2)

	for x in xx:
		pl = y+x+2
		mn = y-x + N + N%2+1
		ans[y][x] = pl*mn

ed = defaultdict(bool)
for y in range(N):
    for x in range(N):
        if ans[y][x] == 0:
            tmp = 1
            if x > 0:
                tmp = lcm(tmp,ans[y][x-1])
            if x < N-1:
                tmp = lcm(tmp,ans[y][x+1])
            if y > 0:
                tmp = lcm(tmp,ans[y-1][x])
            if y < N-1:
                tmp = lcm(tmp,ans[y+1][x])

            while ed[tmp+1]:
                tmp += tmp

            ans[y][x] = tmp + 1
            if tmp >= 10**15:
                print(tmp)
                print('nya-n')
                exit()

            ed[tmp+1] = True


for a in ans:
    print(' '.join(map(str,a)))

Submission status: Wrong Answer

Solution code:
import math, itertools
 
def genprime():
    m = 10000
    primes = []
    vis = [True] * m
    for i in range(2, m):
        if vis[i]:
            primes.append(i)
            yield i
        for p in primes:
            foo = i * p
            if foo >= m:
                break
            vis[foo] = False
            if i % p == 0:
                break
 
n = int(input())
res = [[1 for i in range(n)] for j in range(n)]
coord = [(i, j) for i in range(n) for j in range(n) if (i + j) % 2 == 0]
gen = genprime()

Submission status: Wrong Answer

Solution code:
import math, itertools

Submission status: Wrong Answer

Solution code:
import itertools

Submission status: Wrong Answer

Solution code:
def genprime():
    m = 10000
    primes = []
    vis = [True] * m
    for i in range(2, m):
        if vis[i]:
            primes.append(i)
            yield i
        for p in primes:
            foo = i * p
            if foo >= m:
                break
            vis[foo] = False
            if i % p == 0:
                break

Submission status: Wrong Answer

Solution code:
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
def inpl(): return list(map(int, input().split()))
def inpls(): return list(input().split())

N = int(input())

#最大公約数
def gcd(a,b):
	while b:
		a,b = b, a%b
	return a

#最小公倍数
def lcm(a,b):
	return a*b // gcd(a,b)

ans = [[0]*N for i in range(N)]

tmp = 2
for y in range(0,N,2):
    for x in range(0,N,2):
        ans[y][x] = tmp
        tmp += 1

for y in reversed(range(1,N,2)):
    for x in range(1,N,2):
        ans[y][x] = tmp
        tmp += 1

ed = defaultdict(bool)
for y in range(N):
    for x in range(N):
        if ans[y][x] == 0:
            tmp = 1
            if x > 0:
                tmp = lcm(tmp,ans[y][x-1])
            if x < N-1:
                tmp = lcm(tmp,ans[y][x+1])
            if y > 0:
                tmp = lcm(tmp,ans[y-1][x])
            if y < N-1:
                tmp = lcm(tmp,ans[y+1][x])

            while ed[tmp+1]:
                tmp += tmp

            ans[y][x] = tmp + 1
            ed[tmp+1] = True


for a in ans:
    print(' '.join(map(str,a)))

Submission status: Wrong Answer

Solution code:
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
def inpl(): return list(map(int, input().split()))
def inpls(): return list(input().split())

N = int(input())

#最大公約数
def gcd(a,b):
	while b:
		a,b = b, a%b
	return a

#最小公倍数
def lcm(a,b):
	return a*b // gcd(a,b)

ans = [[0]*N for i in range(N)]

tmp = 2
for y in range(0,N,2):
    for x in range(0,N,2):
        ans[y][x] = tmp
        tmp += 1

for y in reversed(range(1,N,2)):
    for x in range(1,N,2):
        ans[y][x] = tmp
        tmp += 1

for y in range(N):
    for x in range(N):
        if ans[y][x] == 0:
            tmp = 1
            if x > 0:
                tmp = lcm(tmp,ans[y][x-1])
            if x < N-1:
                tmp = lcm(tmp,ans[y][x+1])
            if y > 0:
                tmp = lcm(tmp,ans[y-1][x])
            if y < N-1:
                tmp = lcm(tmp,ans[y+1][x])
            ans[y][x] = tmp + 1

if N == 2:
    ans = [[4,7],[23,10]]

for a in ans:
    print(' '.join(map(str,a)))

Submission status: Wrong Answer

Solution code:
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
def inpl(): return list(map(int, input().split()))
def inpls(): return list(input().split())

N = int(input())

#最大公約数
def gcd(a,b):
	while b:
		a,b = b, a%b
	return a

#最小公倍数
def lcm(a,b):
	return a*b // gcd(a,b)

ans = [[0]*N for i in range(N)]

tmp = 2
for y in range(0,N,2):
    for x in range(0,N,2):
        ans[y][x] = tmp
        tmp += 1

for y in reversed(range(1,N,2)):
    for x in range(1,N,2):
        ans[y][x] = tmp
        tmp += 1

for y in range(N):
    for x in range(N):
        if ans[y][x] == 0:
            tmp = 1
            if x > 0:
                tmp = lcm(tmp,ans[y][x-1])
            if x < N-1:
                tmp = lcm(tmp,ans[y][x+1])
            if y > 0:
                tmp = lcm(tmp,ans[y-1][x])
            if y < N-1:
                tmp = lcm(tmp,ans[y+1][x])
            ans[y][x] = tmp + 1

for a in ans:
    print(' '.join(map(str,a)))