#include <bits/stdc++.h>
#include "Alice.h"
using namespace std;
using ll = int64_t;
std::vector<std::pair<int,int>> Alice(){
ll X = setN(5000);
vector<int> nums = {23, 43, 89, 256, 362, 446, 522, 555, 578, 612, 691, 714, 736, 811, 927, 957, 998, 1028, 1059, 1121, 1163, 1228, 1296, 1412, 1460, 1532, 1646, 1770, 1867, 1889, 1909, 2082, 2150, 2192, 2272, 2322, 2344, 2437, 2481, 2671, 2704, 2771, 2795, 2875, 2930, 2964, 3040, 3095, 3150, 3231, 3274, 3296, 3330, 3402, 3452, 3508, 3557, 3617, 3670, 3697};
int back = 5000;
set<pair<int, int>> edges;
for (int i = 1; i < 5000; i++) edges.insert({i, i + 1});
for (int i = 1; i < 5000; i++) {
auto it = lower_bound(nums.begin(), nums.end(), i);
if (it != nums.end() && *it == i) {
ll ind = it - nums.begin();
if (!((X >> ind) & 1)) continue;
for (int j = 0; j < 18; j++) {
edges.erase({back - 1, back});
edges.insert({i, back});
back--;
}
}
}
vector<pair<int, int>> vec;
for (auto [u, v] : edges) vec.push_back({u, v});
return vec;
}
#include <bits/stdc++.h>
#include "Bob.h"
using namespace std;
using ll = int64_t;
long long Bob(std::vector<std::pair<int,int>> V){
vector<int> deg(5001, 0);
for (auto [u, v] : V) {
deg[u]++;
deg[v]++;
}
vector<int> nums = {23, 43, 89, 256, 362, 446, 522, 555, 578, 612, 691, 714, 736, 811, 927, 957, 998, 1028, 1059, 1121, 1163, 1228, 1296, 1412, 1460, 1532, 1646, 1770, 1867, 1889, 1909, 2082, 2150, 2192, 2272, 2322, 2344, 2437, 2481, 2671, 2704, 2771, 2795, 2875, 2930, 2964, 3040, 3095, 3150, 3231, 3274, 3296, 3330, 3402, 3452, 3508, 3557, 3617, 3670, 3697};
ll ans = 0;
for (ll i = 0; i < 60; i++) {
ll x = nums[i];
if (deg[x] > 2) ans |= (1LL << i);
}
return ans;
}
