#include <bits/stdc++.h>
using namespace std;
#ifdef tabr
#include "library/debug.cpp"
#else
#define debug(...)
#endif
#ifdef tabr
function<int(int, int)> getDistance;
#else
#include "rail.h"
#endif
void findLocation(int n, int first, int loc[], int stype[]) {
loc[0] = 0;
stype[0] = 1;
vector<int> d0(n);
for (int i = 1; i < n; i++) {
d0[i] = getDistance(0, i);
}
int pos0 = 0;
int pos1 = (int) (min_element(d0.begin() + 1, d0.end()) - d0.begin());
loc[pos1] = d0[pos1];
stype[pos1] = 2;
vector<int> d1(n);
d1[0] = d0[pos1];
for (int i = 1; i < n; i++) {
if (i != pos1) {
d1[i] = getDistance(pos1, i);
}
}
vector<int> left;
vector<int> right;
left.emplace_back(pos0);
right.emplace_back(pos1);
for (int i = 1; i < n; i++) {
if (i == pos1) {
continue;
} else if (d1[i] + d0[pos1] == d0[i]) {
left.emplace_back(i);
} else {
right.emplace_back(i);
}
}
sort(left.begin(), left.end(), [&](int i, int j) {
return d0[i] < d0[j];
});
sort(right.begin(), right.end(), [&](int i, int j) {
return d0[i] < d0[j];
});
reverse(left.begin(), left.end());
while (left.back() != pos0) {
int i = left.back();
loc[i] = d0[i] - 2 * d1[i];
stype[i] = 1;
left.pop_back();
}
reverse(left.begin(), left.end());
debug(left);
debug(right);
int j = left[0];
left.erase(left.begin());
vector<int> l1;
l1.emplace_back(j);
for (int i : left) {
int c = getDistance(j, i);
int p = d0[pos1] - d1[j] + c;
int l = -1;
for (int k : l1) {
if (p - loc[k] >= 0 && (l == -1 || p - loc[k] <= p - loc[l])) {
l = k;
}
}
if (l != -1 && d1[i] != d1[l] + (p - loc[l])) {
loc[i] = d0[pos1] - d1[i];
stype[i] = 1;
j = i;
l1.emplace_back(j);
} else {
loc[i] = p;
stype[i] = 2;
}
}
j = right[0];
right.erase(right.begin());
vector<int> r2;
r2.emplace_back(j);
for (int i : right) {
int c = getDistance(j, i);
int p = d0[j] - c;
int l = -1;
for (int k : r2) {
if (loc[k] - p >= 0 && (l == -1 || loc[k] - p <= loc[l] - p)) {
l = k;
}
}
if (l != -1 && d0[i] != d0[l] + (loc[l] - p)) {
loc[i] = d0[i];
stype[i] = 2;
j = i;
r2.emplace_back(j);
} else {
loc[i] = p;
stype[i] = 1;
}
}
for (int i = 0; i < n; i++) {
loc[i] += first;
}
}
#ifdef tabr
mt19937 rng((unsigned int) chrono::steady_clock::now().time_since_epoch().count());
int rand_int(int a, int b) { // [a, b]
return uniform_int_distribution<int>(a, b)(rng);
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
const int n = 5;
const int m = 100;
int loc[n] = {};
int stype[n] = {};
vector<int> a(n);
while (true) {
for (int i = 0; i < n; i++) {
a[i] = rand_int(0, m);
}
auto b = a;
sort(b.begin(), b.end());
b.resize(unique(b.begin(), b.end()) - b.begin());
if (b.size() == a.size() && max_element(a.begin(), a.end()) != a.begin()) {
break;
}
}
vector<int> b(n);
for (int i = 0; i < n; i++) {
b[i] = rand_int(1, 2);
}
b[max_element(a.begin(), a.end()) - a.begin()] = 2;
b[min_element(a.begin(), a.end()) - a.begin()] = 1;
b[0] = 1;
vector<vector<int>> d(n, vector<int>(n));
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i == j) {
d[i][j] = 0;
} else if (a[i] < a[j]) {
d[i][j] = a[j] - a[i];
if (b[i] == 2) {
int c = (int) 1e9;
for (int k = 0; k < n; k++) {
if (b[k] == 1 && a[k] < a[i]) {
c = min(c, a[i] - a[k]);
}
}
d[i][j] += c * 2;
}
if (b[j] == 1) {
int c = (int) 1e9;
for (int k = 0; k < n; k++) {
if (b[k] == 2 && a[k] > a[j]) {
c = min(c, a[k] - a[j]);
}
}
d[i][j] += c * 2;
}
} else {
d[i][j] = a[i] - a[j];
if (b[j] == 2) {
int c = (int) 1e9;
for (int k = 0; k < n; k++) {
if (b[k] == 1 && a[k] < a[j]) {
c = min(c, a[j] - a[k]);
}
}
d[i][j] += c * 2;
}
if (b[i] == 1) {
int c = (int) 1e9;
for (int k = 0; k < n; k++) {
if (b[k] == 2 && a[k] > a[i]) {
c = min(c, a[k] - a[i]);
}
}
d[i][j] += c * 2;
}
}
}
}
int cnt = 0;
getDistance = [&](int i, int j) {
cnt++;
return d[i][j];
};
findLocation(n, a[0], loc, stype);
bool ok = true;
for (int i = 0; i < n; i++) {
if (a[i] != loc[i] || b[i] != stype[i]) {
ok = false;
}
}
debug(ok, cnt, cnt <= 3 * (n - 1));
for (int i = 0; i < n; i++) {
debug(i);
debug(loc[i], stype[i]);
debug(a[i], b[i]);
}
debug(d);
return 0;
}
#endif
