// CF template, version 3.0
#include <bits/stdc++.h>
#include "Alice.h"
using namespace std;
#define improvePerformance ios_base::sync_with_stdio(false); cin.tie(0)
#define getTest int t; cin >> t
#define eachTest for (int _var=0;_var<t;_var++)
#define get(name) int (name); cin >> (name)
#define out(o) cout << (o)
#define getList(cnt, name) vector<int> (name); for (int _=0;_<(cnt);_++) { get(a); (name).push_back(a); }
#define sortl(name) sort((name).begin(), (name).end())
#define rev(name) reverse((name).begin(), (name).end())
#define forto(name, var) for (int (var) = 0; (var) < (name); (var)++)
#define decision(b) if (b){out("YES");}else{out("NO");}
//#define int long long int
template <typename T, typename I>
struct segtree {
int n;
vector<T> tree;
vector<I> initial;
T id;
segtree(int i_n, vector<I> i_initial, T i_id): n(i_n), initial(i_initial), id(i_id) {
tree.resize(4 * n);
}
T conquer(T left, T right) {
// write your conquer function
}
T value(I inp) {
// write your value function
}
void build(int v, int l, int r) {
if (l == r) tree[v] = value(initial[l]);
else {
int middle = (l + r) / 2;
build(2 * v, l, middle);
build(2 * v + 1, middle + 1, r);
tree[v] = conquer(tree[2 * v], tree[2 * v + 1]);
}
}
void upd(int v, int l, int r, int i, I x) {
if (l == r) tree[v] = value(x);
else {
int middle = (l + r) / 2;
if (middle >= i) upd(2 * v, l, middle, i, x);
else upd(2 * v + 1, middle + 1, r, i, x);
tree[v] = conquer(tree[2 * v], tree[2 * v + 1]);
}
}
T query(int v, int l, int r, int ql, int qr) {
if (ql <= l && r <= qr) return tree[v];
else if (r < ql || qr < l) return id;
int middle = (l + r) / 2;
T left = query(2 * v, l, middle, ql, qr);
T right = query(2 * v + 1, middle + 1, r, ql, qr);
return conquer(left, right);
}
};
// vector<int>
/*long long setN(int n) {
get(X);
return X;
}*/
vector<pair<int, int>> Alice() {
long long X = setN(5000);
vector<pair<int, int>> res;
if (X == 25000000) return res;
if (X % 5001 == 0) {
int j = X / 5001;
forto(5000, i) {
if (i == j) continue;
res.push_back({i + 1, j + 1});
}
return res;
}
int a = X / 5000;
int b = X % 5000;
if (a < b) {
forto(5000, i) {
if (i == a) continue;
res.push_back({i + 1, a + 1});
}
forto(5000, i) {
if (i == a || i == b) continue;
res.push_back({i + 1, b + 1});
}
} else {
vector<int> left;
forto(5000, i) if (i != a && i != b) left.push_back(i);
forto(3000, i) res.push_back({a + 1, left[i] + 1});
forto(3000, i) res.push_back({b + 1, left[4997 - i] + 1});
}
return res;
}
// CF template, version 3.0
#include <bits/stdc++.h>
using namespace std;
#define improvePerformance ios_base::sync_with_stdio(false); cin.tie(0)
#define getTest int t; cin >> t
#define eachTest for (int _var=0;_var<t;_var++)
#define get(name) int (name); cin >> (name)
#define out(o) cout << (o)
#define getList(cnt, name) vector<int> (name); for (int _=0;_<(cnt);_++) { get(a); (name).push_back(a); }
#define sortl(name) sort((name).begin(), (name).end())
#define rev(name) reverse((name).begin(), (name).end())
#define forto(name, var) for (int (var) = 0; (var) < (name); (var)++)
#define decision(b) if (b){out("YES");}else{out("NO");}
//#define int long long int
template <typename T, typename I>
struct segtree {
int n;
vector<T> tree;
vector<I> initial;
T id;
segtree(int i_n, vector<I> i_initial, T i_id): n(i_n), initial(i_initial), id(i_id) {
tree.resize(4 * n);
}
T conquer(T left, T right) {
// write your conquer function
}
T value(I inp) {
// write your value function
}
void build(int v, int l, int r) {
if (l == r) tree[v] = value(initial[l]);
else {
int middle = (l + r) / 2;
build(2 * v, l, middle);
build(2 * v + 1, middle + 1, r);
tree[v] = conquer(tree[2 * v], tree[2 * v + 1]);
}
}
void upd(int v, int l, int r, int i, I x) {
if (l == r) tree[v] = value(x);
else {
int middle = (l + r) / 2;
if (middle >= i) upd(2 * v, l, middle, i, x);
else upd(2 * v + 1, middle + 1, r, i, x);
tree[v] = conquer(tree[2 * v], tree[2 * v + 1]);
}
}
T query(int v, int l, int r, int ql, int qr) {
if (ql <= l && r <= qr) return tree[v];
else if (r < ql || qr < l) return id;
int middle = (l + r) / 2;
T left = query(2 * v, l, middle, ql, qr);
T right = query(2 * v + 1, middle + 1, r, ql, qr);
return conquer(left, right);
}
};
// vector<int>
long long Bob(vector<pair<int, int>> edges) {
if (edges.empty()) return 25000000;
vector<int> deg(5000);
for (auto edge: edges) deg[edge.first - 1]++, deg[edge.second - 1]++;
int heavy = 0;
for (int d: deg) heavy += d >= 100;
if (heavy == 1) {
forto(5000, i) if (deg[i] >= 100) return 5001 * i;
}
int two = 0;
for (int d: deg) two += d >= 2;
int a = -1;
int b = -1;
forto(5000, i) {
if (deg[i] >= 100) {
if (a == -1) a = i;
else b = i;
}
}
if (two >= 2000) return a * 5000 + b;
return 5000 * b + a;
}
