#include "scales.h"
#include <bits/stdc++.h>
using namespace std;
#define pii pair<int, int>
#define ff first
#define ss second
#define pb push_back
void init(int T) {
}
/*
getHeaviest()
getLightest()
getMedian()
getNextLightest()
*/
vector<pair<int, vector<int>>> clues; // {type, {answer, [query elements]}}
vector<int> perm = {0, 1, 2, 3, 4, 5, 6};
vector<vector<int>> FindAllPossible() {
// cerr << "CURRENT CLUES:\n";
// for (pair<int, vector<int>> &cur : clues) {
// cerr << cur.ff << " | ";
// for (int &x : cur.ss) cerr << x << ' ';
// cerr << endl;
// }
sort(perm.begin(), perm.end());
vector<vector<int>> res = {};
do {
bool valid = true;
for (pair<int, vector<int>> &cur : clues) {
// cerr << "CLUE " << cur.ff << ' ';
// for (int &x : cur.ss) cerr << x << ' '; cerr << endl;
if (cur.ff == 1) {
for (int i = 1; i <= 3; i++) {
if (cur.ss[0] == cur.ss[i]) continue;
valid &= (perm[cur.ss[0]] > perm[cur.ss[i]]);
}
}
if (cur.ff == 2) {
for (int i = 1; i <= 3; i++) {
if (cur.ss[0] == cur.ss[i]) continue;
valid &= (perm[cur.ss[0]] < perm[cur.ss[i]]);
}
}
if (cur.ff == 3) {
int cnt = 0;
for (int i = 1; i <= 3; i++) {
if (cur.ss[0] == cur.ss[i]) continue;
cnt += (perm[cur.ss[0]] < perm[cur.ss[i]]);
}
valid &= (cnt == 1);
}
if (cur.ff == 4) {
bool allsmaller = true;
for (int i = 1; i <= 3; i++) {
allsmaller &= (perm[cur.ss[i]] < perm[cur.ss[4]]);
}
if (allsmaller) {
for (int i = 1; i <= 3; i++) {
if (cur.ss[0] == cur.ss[i]) continue;
valid &= (perm[cur.ss[i]] > perm[cur.ss[0]]);
}
} else {
valid &= (perm[cur.ss[0]] > perm[cur.ss[4]]);
for (int i = 1; i <= 3; i++) {
if (cur.ss[0] == cur.ss[i]) continue;
valid &= (perm[cur.ss[i]] < perm[cur.ss[4]] || perm[cur.ss[i]] > perm[cur.ss[0]]);
}
}
}
if (!valid) break;
}
if (valid) {
// cerr << "FOUND ";
// for (int &x : perm) cerr << x << ' ';
// cerr << endl;
res.pb(perm);
}
} while (next_permutation(perm.begin() + 1, perm.end()));
return res;
}
void Answer(vector<int> v) {
int ans[6];
for (int i = 1; i <= 6; i++) ans[v[i] - 1] = i;
answer(ans);
}
int Heaviest(int a, int b, int c = 0) {
if (c == 0) c = (min(a, b) != 1 ? 1 : max(a, b) != 2 ? 2 : 3);
int res = getHeaviest(a, b, c);
clues.pb({1, {res, a, b, c}});
return res;
}
int Lightest(int a, int b, int c = 0) {
if (c == 0) c = (min(a, b) != 1 ? 1 : max(a, b) != 2 ? 2 : 3);
int res = getLightest(a, b, c);
clues.pb({2, {res, a, b, c}});
return res;
}
int Median(int a, int b, int c) {
int res = getMedian(a, b, c);
clues.pb({3, {res, a, b, c}});
return res;
}
int NextLightest(int a, int b, int c, int d) {
int res = getNextLightest(a, b, c, d);
clues.pb({4, {res, a, b, c, d}});
return res;
}
/*
getHeaviest()
getLightest()
getMedian()
getNextLightest()
*/
int TryHeaviest(int a, int b, int c) {
int res = 0;
clues.pb({1, {a, a, b, c}}); res = max(res, (int)FindAllPossible().size()); clues.pop_back();
clues.pb({1, {b, a, b, c}}); res = max(res, (int)FindAllPossible().size()); clues.pop_back();
clues.pb({1, {c, a, b, c}}); res = max(res, (int)FindAllPossible().size()); clues.pop_back();
return res;
}
int TryLightest(int a, int b, int c) {
int res = 0;
clues.pb({2, {a, a, b, c}}); res = max(res, (int)FindAllPossible().size()); clues.pop_back();
clues.pb({2, {b, a, b, c}}); res = max(res, (int)FindAllPossible().size()); clues.pop_back();
clues.pb({2, {c, a, b, c}}); res = max(res, (int)FindAllPossible().size()); clues.pop_back();
return res;
}
int TryMedian(int a, int b, int c) {
int res = 0;
clues.pb({3, {a, a, b, c}}); res = max(res, (int)FindAllPossible().size()); clues.pop_back();
clues.pb({3, {b, a, b, c}}); res = max(res, (int)FindAllPossible().size()); clues.pop_back();
clues.pb({3, {c, a, b, c}}); res = max(res, (int)FindAllPossible().size()); clues.pop_back();
return res;
}
int TryNextLightest(int a, int b, int c, int d) {
int res = 0;
clues.pb({4, {a, a, b, c, d}}); res = max(res, (int)FindAllPossible().size()); clues.pop_back();
clues.pb({4, {b, a, b, c, d}}); res = max(res, (int)FindAllPossible().size()); clues.pop_back();
clues.pb({4, {c, a, b, c, d}}); res = max(res, (int)FindAllPossible().size()); clues.pop_back();
return res;
}
int TestTwo(pair<int, vector<int>> lhs, vector<pair<int, vector<int>>> rhs) {
int res = 0;
for (int i = 1; i < (int)lhs.ss.size(); i++) {
lhs.ss[0] = lhs.ss[i];
clues.pb(lhs);
for (int j = 1; j < (int)rhs[i - 1].ss.size(); j++) {
rhs[i - 1].ss[0] = rhs[i - 1].ss[i];
clues.pb(rhs[i - 1]);
res = max(res, (int)FindAllPossible().size());
clues.pop_back();
}
clues.pop_back();
}
return res;
}
mt19937 rng(time(NULL));
int GetRand(int x) {
return (int)(rng() % x);
}
void orderCoins() {
clues.clear();
// try pure exhaust?
vector<vector<int>> fin = FindAllPossible();
while (fin.size() > 1) {
// cerr << "Current size: " << fin.size() << ", ";
// cerr << "Current queries: " << clues.size() << endl;
int cursz = (int)fin.size(), res;
vector<int> nxtquery;
vector<vector<int>> nxtqueries;
for (int a = 1; a <= 6; a++) {
for (int b = a + 1; b <= 6; b++) {
for (int c = b + 1; c <= 6; c++) {
res = TryHeaviest(a, b, c);
if (res <= cursz) {
if (res < cursz) nxtqueries.clear();
nxtqueries.pb({1, a, b, c});
cursz = res;
}
res = TryLightest(a, b, c);
if (res <= cursz) {
if (res < cursz) nxtqueries.clear();
nxtqueries.pb({2, a, b, c});
cursz = res;
}
res = TryMedian(a, b, c);
if (res <= cursz) {
if (res < cursz) nxtqueries.clear();
nxtqueries.pb({3, a, b, c});
cursz = res;
}
for (int d = 1; d <= 6; d++) {
if (d == a || d == b || d == c) continue;
res = TryNextLightest(a, b, c, d);
if (res <= cursz) {
if (res < cursz) nxtqueries.clear();
nxtqueries.pb({4, a, b, c, d});
cursz = res;
}
}
}
}
}
// cout << "Queries: " << cursz << endl;
// for (vector<int> &cur : nxtqueries) {
// for (int &x : cur) cout << x << ' ';
// cout << endl;
// }
// return;
shuffle(nxtqueries.begin(), nxtqueries.end(), rng);
nxtquery = nxtqueries.front();
for (vector<int> &cur : nxtqueries) {
if (cur[0] == 4) nxtquery = cur;
else if (cur[3] < nxtquery[3]) nxtquery = cur;
}
if (nxtquery.front() == 1) Heaviest(nxtquery[1], nxtquery[2], nxtquery[3]);
if (nxtquery.front() == 2) Lightest(nxtquery[1], nxtquery[2], nxtquery[3]);
if (nxtquery.front() == 3) Median(nxtquery[1], nxtquery[2], nxtquery[3]);
if (nxtquery.front() == 4) NextLightest(nxtquery[1], nxtquery[2], nxtquery[3], nxtquery[4]);
fin = FindAllPossible();
}
Answer(fin.front());
}
/*
15 edges to consider (know all -> must can sort)
full sol: 6 queries (by math)
(current sol: 7 queries)
full sol is consider 2 queries at once (?)
*/
