Manhattan sightseeing

import math
n = int(input())
q = []
x = 0
y = 0
maxa2 = -math.inf
mina2 = math.inf
minb2 = math.inf
maxb2 = -math.inf
for i in range(n):
    a, b = map(int, input().split())
    q.append([a, b])
    a2 = a - b
    b2 = a + b
    # print(a2, b2)
    if a2 < mina2:
        mina2 = a2
    if a2 > maxa2:
        maxa2 = a2
    if b2 < minb2:
        minb2 = b2
    if b2 > maxb2:
        maxb2 = b2
max_00 = -math.inf
max_01 = -math.inf
max_10 = -math.inf
max_11 = -math.inf
ca = (maxa2 + mina2)
cb = (maxb2 + minb2)
x = (ca + cb) // 4
y = (cb - ca) // 4

for i in range(n):
    a, b = q[i]
    dist_00 = abs(a - x) + abs(b - y)
    dist_01 = abs(a - x - 1) + abs(b - y)
    dist_10 = abs(a - x) + abs(b - y - 1)
    dist_11 = abs(a - x - 1) + abs(b - y - 1)
    max_00 = max(dist_00, max_00)
    max_01 = max(dist_01, max_01)
    max_10 = max(dist_10, max_10)
    max_11 = max(dist_11, max_11)
minn = min([max_00, max_01, max_10, max_11])
if max_00 == minn:
    print(x, y)
elif max_01 == minn:
    print(x, y + 1)
elif max_10 == minn:
    print(x + 1, y)
else:
    print(x + 1, y + 1)

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED

Test 18

Verdict: ACCEPTED

Test 19

Verdict: ACCEPTED

Test 20

Verdict: ACCEPTED

Test 21

Verdict: ACCEPTED

Test 22

Verdict: ACCEPTED

Test 23

Verdict: ACCEPTED

Test 24

Verdict: ACCEPTED

Test 25

Verdict: ACCEPTED

Test 26

Verdict: ACCEPTED

Test 27

Verdict: ACCEPTED

Test 28

Verdict: ACCEPTED

Test 29

Verdict: ACCEPTED

Test 30

Verdict: ACCEPTED

Test 31

Verdict: ACCEPTED

Test 32

Verdict: ACCEPTED

Test 33

Verdict: ACCEPTED

Test 34

Verdict: ACCEPTED

Test 35

Verdict: ACCEPTED

Test 36

Verdict: ACCEPTED

Test 37

Verdict: ACCEPTED

Test 38

Verdict: ACCEPTED

Test 39

Verdict: ACCEPTED

Test 40

Verdict: ACCEPTED

Test 41

Verdict: ACCEPTED

Test 42

Verdict: ACCEPTED

Test 43

Verdict: ACCEPTED

Test 44

Verdict: ACCEPTED

Test 45

Verdict: ACCEPTED

Test 46

Verdict: ACCEPTED

Test 47

Verdict: ACCEPTED

Test 48

Verdict: ACCEPTED

Test 49

Verdict: ACCEPTED

Test 50

Verdict: ACCEPTED

Test 51

Verdict: ACCEPTED

Test 52

Verdict: ACCEPTED

Test 53

Verdict: ACCEPTED

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Verdict: ACCEPTED

Test 55

Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

Test 62

Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

Test 65

Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

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Verdict: ACCEPTED

Test 69

Verdict: ACCEPTED

Test 70

Verdict: ACCEPTED

Test 71

Verdict: ACCEPTED

Test 72

Verdict: ACCEPTED

Test 73

Verdict: ACCEPTED

Test 74

Verdict: ACCEPTED

Test 75

Verdict: ACCEPTED

Test 76

Verdict: ACCEPTED

Test 77

Verdict: ACCEPTED