Manhattan sightseeing

// #ifdef ONLINE_JUDGE
// #pragma GCC optimize("O3,unroll-loops")
// #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
// #endif
#include "bits/stdc++.h"
#define fast ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define fill(arr,val) memset(arr,val,sizeof(arr))
#define FOR(i, a, b) for(__typeof(b) i = a, _b = b; i <= _b; ++i)
#define FORD(i, a, b) for(__typeof(a) i = a, _b = b; i >= _b; --i)
#define ALL(a) (a).begin(), (a).end()
#define YES cout << "YES\n"
#define NO cout << "NO\n"
#define ll long long
#define fi first
#define se second
#define pb push_back
#define pf push_front
#define ii pair<int,int>
#define iii pair<int,pair<int,int>>
#define dq deque<int>
#define nend '\n'
using namespace std;

const ll inf = 1e18;
const int dx[] = {1,0,-1,0};
const int dy[] = {0,1,0,-1};
const int MOD = 1e9 + 7;
const ll hashi = 2e9 + 11;

void init_code() {
    fast;
    // #ifndef ONLINE_JUDGE
    // freopen("input.txt", "r", stdin);
    // freopen("output.txt", "w", stdout);
    // #endif
}
int n;
ll umin=inf, umax=-inf, vmin=inf, vmax=-inf;
ll U, V;

// rotate 45 deg: u=x+y, v=x-y  ->  |dx|+|dy| = max(|du|,|dv|)
// so "distance <= R" is a square: u in [umax-R, umin+R], v in [vmax-R, vmin+R]
// (a,b) is an integer point only if u and v have the same parity
bool check(ll R) {
    ll lu=umax-R, hu=umin+R, lv=vmax-R, hv=vmin+R;
    if (lu>hu || lv>hv) return false;
    for (ll u=lu; u<=min(hu,lu+1); u++) for (ll v=lv; v<=min(hv,lv+1); v++)
        if (((u^v)&1)==0) { U=u; V=v; return true; }
    return false;
}

void solve() {
    cin >> n;
    FOR(i,1,n) {
        ll x,y; cin >> x >> y;
        umin=min(umin,x+y); umax=max(umax,x+y);
        vmin=min(vmin,x-y); vmax=max(vmax,x-y);
    }
    ll R=max((umax-umin+1)/2,(vmax-vmin+1)/2);
    if (!check(R)) check(R+1);
    cout << (U+V)/2 << ' ' << (U-V)/2 << nend;
}

int main() {
    init_code();

    int t = 1;
    // cin >> t;
    while (t--) {
        solve();
    }

    return 0;
}

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

Test 54

Verdict: ACCEPTED

Test 55

Verdict: ACCEPTED

Test 56

Verdict: ACCEPTED

Test 57

Verdict: ACCEPTED

Test 58

Verdict: ACCEPTED

Test 59

Verdict: ACCEPTED

Test 60

Verdict: ACCEPTED

Test 61

Verdict: ACCEPTED

Test 62

Verdict: ACCEPTED

Test 63

Verdict: ACCEPTED

Test 64

Verdict: ACCEPTED

Test 65

Verdict: ACCEPTED

Test 66

Verdict: ACCEPTED

Test 67

Verdict: ACCEPTED

Test 68

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