#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <random>
#include "combo.h"
using namespace std;
using namespace __gnu_pbds;
#pragma GCC optimize("O3,Ofast,unroll-loops")
//#pragma GCC target("popcnt")
//#define int long long
#define ll long long
#define ld long double
#define endl '\n'
#define rep(i,n) for(int i=0;i<n;i++)
#define pii pair<int,int>
#define debug(...) printf(__VA_ARGS__)
//#define debug(...)
#define trace(x) cout<<#x<<"="<<x<<endl;
//#define trace(x)
#define vi vector<int>
#define popcnt(x) (int)__builtin_popcountll(x)
#define vpii vector<pii >
#define vaii vector<array<int,2>>
#define vvi vector<vector<int> >
#define umap unordered_map
#define uset unordered_set
#define mk make_pair
#define pb push_back
#define pob pop_back
#define _ <<' '<<
#define all(x) x.begin(),x.end()
#define allr(x) x.rbegin(),x.rend()
#define read(x) for (auto& zu: (x)) cin >> zu;
#define write(x) for (auto& zu: (x))cout << zu<<' '; cout<<endl;
static inline void print(const int &x) {
if (x > 9)print(x / 10);
putchar('0' + x % 10);
}
//template<typename... T>void read(T&... args) {((for (auto &zu: (args)) { cin >> zu; }),...);}
#define F first
#define S second
template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<class T> using ordered_multiset = tree<T, null_type, less_equal<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define mustawa ios::sync_with_stdio(false);cin.tie(nullptr);cout.tie();
#define saudi main
const int inf=1e9+7;
void fa(bool ok){ cout << (ok ? "YES": "NO") << endl;}
int pw(ll a, ll b, ll mod= 1e9 + 7){
a %= mod;
ll res = 1;
while (b > 0) {
if (b&1) {
res = res * a%mod;
}b /= 2;
a = a * a%mod;
}
return res;
}int pwnomod(ll a, ll b){
ll res = 1;
while (b > 0) {
if (b&1) {
res = res * a;
}b /= 2;
a = a * a;
}
return res;
}
inline void usaco(string s) {
freopen((s + ".in").c_str(), "r", stdin);
freopen((s + ".out").c_str(), "w", stdout);
}inline void usaco(string s1,string s2) {
freopen((s1 + ".txt").c_str(), "r", stdin);
freopen((s2 + ".txt").c_str(), "w", stdout);
freopen("err.txt", "w", stderr);
}int inve(int x,int mod=inf){
return pow(x,mod-2);
}
int gcd(int a,int b){
if (b == 0)return a;
return gcd(b, a % b);
}
int lcm(int a, int b){
return (a / gcd(a, b)) * b;
}
//long double log(int base,int x){
// return log2(x)/log(base);
//}
int log(int base,int x){
return (int)(log2(x)/log2(base));
}
int sum(int l,int r) {
if (l > r)swap(l, r);
int a = (l - 1) * l / 2;
int b = r * (r + 1) / 2;
return b - a;
}
const int N=1e6+7;
vi adj[N];
int dp[N];
bool vis[N];
string guess_sequence(int n){
string s="ABXY",ret;
if(press("A"))s="BXY",ret+="A";
else if(press("B"))s="AXY",ret+="B";
else if(press("X"))s="ABY",ret+="X";
else if(press("Y"))s="ABX",ret+="Y";
int cur=1;
for(int i=1;i<n;i++){
for(auto i:s){
string temp=ret+i;
int p=press(temp);
if(p>cur){
cur=p;
ret=temp;
break;
}
}
}return ret;
}
