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#include<bits/stdc++.h>
#define VAR(i,n) __typeof(n) i = (n)
#define loop(i,j,s) for(int i=j;i<s;i++)
#define loopback(i,j,s) for(int i=j;i>=s;i--)
#define foreach(i,c) for(VAR(i,(c).begin());i!=(c).end();i++)
#define pln( x ) cout << x << "\n"
#define ps( x ) cout << x << " "
#define entr cout << "\n"
#define pcnt(i) __builtin_popcount(i)
#define ll long long
#define pb push_back
#define mp make_pair
#define ff first
#define ss second
#define SIZE(c) (c).size()
#define ALL(c) (c).begin(), (c).end()
using namespace std;
typedef vector<int> VI;
typedef pair<int, int> PII;
typedef vector<vector<int> > VVI;
const int INFTY=20000000;
const int MAX=500100;
const int MOD=10000000;

void coutTab(int* tab,int n){
	loop(i,0,n){
		cout<<tab[i]<<" ";
	}
	cout<<"\n";
}

template<class T> void coutVec(vector<T> tab){
	for(T t : tab){
		cout<<t<<" ";
	}
	cout<<"\n";
}
//------------------------------------------

void genLower(int L[10][10], ll seed){
	mt19937_64 rng(seed);
	loop(i,0,10) loop(j,0,10) L[i][j] = 0;
	loop(i,1,10) loop(j,0,i) L[i][j] = rng() & 1;
}

void encode(ll num, int mat[10][10], int L[10][10]){
	loop(i,0,10) loop(j,0,10) mat[i][j] = 0;
	loop(i,1,10) loop(j,0,i) mat[i][j] = L[i][j];
	loop(i,0,10) mat[i][i] = 1;
	int bit = 0;
	loop(i,0,10) loop(j,i+1,10){
		mat[i][j] = (num >> bit) & 1;
		bit++;
	}
}

ll decode(int mat[10][10]){
	ll num = 0;
	int bit = 0;
	loop(i,0,10) loop(j,i+1,10){
		if(mat[i][j]) num |= (1LL << bit);
		bit++;
	}
	return num;
}

int a_g[10][10], L_g[10][10], rSums[10];
bool rAs[10], cAs[10];
int nSols;
const int MAXS = 4;
struct Sol { int rm[10], cm[10]; } sols[MAXS];

void solve(int rm[10], int cm[10], bool ur[10], bool uc[10], int step){
	if(nSols >= MAXS) return;
	if(step == 20){
		loop(i,0,10){
			if(a_g[rm[i]][cm[i]] != 1) return;
			loop(j,0,i) if(a_g[rm[i]][cm[j]] != L_g[i][j]) return;
		}
		memcpy(sols[nSols].rm, rm, 40);
		memcpy(sols[nSols].cm, cm, 40);
		nSols++;
		return;
	}
	if(step % 2 == 0){
		int c = step / 2;
		loop(cj,0,10){
			if(uc[cj]) continue;
			bool ok = true;
			for(int r = c+1; r <= 9 && ok; r++)
				if(rAs[r] && a_g[rm[r]][cj] != L_g[r][c]) ok = false;
			if(!ok) continue;
			if(rAs[c] && a_g[rm[c]][cj] != 1) continue;
			cm[c] = cj; uc[cj] = true; cAs[c] = true;
			solve(rm, cm, ur, uc, step + 1);
			cAs[c] = false; uc[cj] = false;
			if(nSols >= MAXS) return;
		}
	} else {
		int r = 9 - step / 2;
		int knownSum = 1;
		loop(c,0,r) knownSum += L_g[r][c];
		int maxUnk = 9 - r;
		loop(ri,0,10){
			if(ur[ri]) continue;
			if(rSums[ri] < knownSum || rSums[ri] > knownSum + maxUnk) continue;
			bool ok = true;
			loop(c,0,r)
				if(cAs[c] && a_g[ri][cm[c]] != L_g[r][c]){ ok = false; break; }
			if(!ok) continue;
			if(cAs[r] && a_g[ri][cm[r]] != 1) continue;
			rm[r] = ri; ur[ri] = true; rAs[r] = true;
			solve(rm, cm, ur, uc, step + 1);
			rAs[r] = false; ur[ri] = false;
			if(nSols >= MAXS) return;
		}
	}
}

int runSolve(int rm[10], int cm[10]){
	bool ur[10] = {}, uc[10] = {};
	memset(rAs, 0, 10);
	memset(cAs, 0, 10);
	nSols = 0;
	loop(i,0,10){ rSums[i] = 0; loop(j,0,10) rSums[i] += a_g[i][j]; }
	solve(rm, cm, ur, uc, 0);
	return nSols;
}

int main(){
	ios_base::sync_with_stdio(0);
	string role;
	cin >> role;
	ll n; int t;
	cin >> n >> t;
	if(role == "Algosia"){
		loop(q,0,t){
			ll ni; cin >> ni; ni--;
			int mat[10][10], rm[10], cm[10];
			for(int lk = 0; ; lk++){
				ll seed = n ^ ((ll)lk * 999983 + 1000000007);
				int L[10][10];
				genLower(L, seed);
				encode(ni, mat, L);
				memcpy(a_g, mat, sizeof(a_g));
				memcpy(L_g, L, sizeof(L_g));
				if(runSolve(rm, cm) == 1){
					loop(i,0,10){
						loop(j,0,10) cout << mat[i][j];
						cout << "\n";
					}
					cout.flush();
					break;
				}
			}
		}
	} else {
		loop(q,0,t){
			int a[10][10];
			loop(i,0,10){
				string s; cin >> s;
				loop(j,0,10) a[i][j] = s[j] - '0';
			}
			memcpy(a_g, a, sizeof(a_g));
			int rm[10], cm[10];
			ll ans = -1;
			for(int lk = 0; ; lk++){
				ll seed = n ^ ((ll)lk * 999983 + 1000000007);
				int L[10][10];
				genLower(L, seed);
				memcpy(L_g, L, sizeof(L_g));
				if(runSolve(rm, cm) == 1){
					int rec[10][10];
					loop(i,0,10) loop(j,0,10) rec[i][j] = a[sols[0].rm[i]][sols[0].cm[j]];
					ans = decode(rec) + 1;
					break;
				}
			}
			pln(ans);
			cout.flush();
		}
	}
}