#include "towns.h"
#include <bits/stdc++.h>
#define Loop(x,l,r) for (ll x = (l); x < (r); ++x)
#define LoopR(x,l,r) for (ll x = (r)-1; x >= (l); --x)
typedef std::pair<int,int> pii;
typedef long long ll;
using namespace std;
const int N = 120;
int dis0[N], disa[N];//, disb[N];
int dis[N][N];
int cnt;
namespace dsu {
int par[N];
int sz[N];
void init() {
fill(par, par+N, -1);
fill(sz, sz+N, 1);
}
int rt(int v) { return par[v] == -1? v: (par[v] = rt(par[v])); }
void unite(int v, int u) {
//v = rt(v);
//u = rt(u);
//if (sz[v] < sz[u])
// swap(v, u);
sz[v] += sz[u];
par[u] = v;
}
}
int get(int i, int j)
{
if (i == j)
return 0;
if (i > j)
swap(i, j);
if (!dis[i][j]) {
++cnt;
dis[i][j] = getDistance(i, j);
}
return dis[i][j];
}
int get2(int a, int v, int b)
{
return (get(a, v) + get(a, b) - get(v, b))/2;
}
int find_hub(int a, int b, int n, int r)
{
if (get(a, b) == r*2)
return r;
bool x = 0, y = 0;
vector<int> X, Y;
Loop (i,0,n) {
if (get2(a, i, 0) == r)
x = 1;
if (get2(a, i, 0) == get(a, b) - r)
y = 1;
int x = get2(a, i, 0);
int y = get(a, b) - x;
(x < y? Y: X).push_back(i);
}
if (!x)
return get(a, b) - r;
if (!y)
return r;
if (X.size()*2 > n)
return r;
if (X.size()*2 == n)
return -1;
return get(a, b) - r;
}
int hubDistance(int n, int sub) {
memset(dis, 0, sizeof(dis));
cnt = 0;
Loop (i,0,n)
dis0[i] = get(0, i);
int a = max_element(dis0, dis0+n) - dis0;
Loop (i,0,n)
disa[i] = get(a, i);
int b = max_element(disa, disa+n) - disa;
//Loop (i,0,n)
// disb[i] = get(b, i);
int ans = 1e9;
Loop (i,0,n) {
int x = get2(a, i, 0);
int y = disa[b] - x;
ans = min(ans, max(x, y));
}
int v = find_hub(a, b, n, ans);
if (v == -1)
return ans;
vector<int> L, M, R;
Loop (i,0,n) {
(get2(a, i, 0) < v? L:
get2(a, i, 0) > v? R:
M).push_back(i);
}
if (L.size()*2 > n || R.size()*2 > n)
return -ans;
if (M.size()*2 <= n)
return ans;
auto same = [&](int i, int j) {
return get2(i, a, 0) + get2(j, a, 0) != get(i, j);
};
vector<int> M1, M2, M2h;
for (int i = 0; i < M.size(); i += 2) {
if (i+1 == M.size()) {
M2.push_back(M[i]);
} else if (same(M[i], M[i+1])) {
M2.push_back(M[i]);
M2.push_back(M[i+1]);
} else {
M1.push_back(M[i]);
M1.push_back(M[i+1]);
}
}
int x = -1, cnt = 0;
for (int i = 0; i < M2.size(); i += 2) {
int z = M2[i];
if (cnt == 0 || same(x, z)) {
x = z;
++cnt;
} else {
--cnt;
}
}
if (cnt == 0)
return ans;
cnt = 0;
for (int i = 0; i < M2.size(); i += 2) {
if (same(M2[i], x)) {
++cnt;
if (i+1 < M2.size())
++cnt;
}
}
if (cnt*2 <= M2.size())
return ans;
for (int y : M1)
cnt += same(x, y);
if (cnt*2 <= n)
return ans;
return -ans;
}
