task 2

int imp (int a, int b) {
	if (a == 1 && b == 0) return 0;
	return 1;
}

signed main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);
	fr (x, 2) {
		fr (y, 2) {
			fr (z, 2) {
				fr (w, 2) {
					int a = imp (y, w);
					int b = imp (x, 1 - z);
					int c = a == b;
					int d = x || w;
					int e = c && d;
					cerr << x << ' ' << y << ' ' << z << ' '  << w << ' ' << e << '\n';
				}
			}
		}
	}
}

task 5

int kek (int n) {
	vector<int> goo;
	while (n) {
		goo.pb (n % 2);
		n /= 2;
	}
	reverse (all (goo));
	while (!goo.empty () && goo.back () == 0) goo.pop_back ();
	int ans = 0;
	fr (i, sz (goo)) ans += (1<<i) * goo[i];
	return ans;
}

signed main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);
	for (int i = 100; i > 0; --i) {
		if (kek (i) == 13) {
			dbg (i);
			exit (0);
		}
	}
}

task 6

int kek (int s) {
	int n = 1;
	while (s > 200) {
		s -= 15;
		n += 3;
	}
	return n;
}

signed main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);
	for (int i = 10000; i > 0; --i) {
		if (kek (i) == 46) {
			dbg (i);
			exit (0);
		}
	}
}

task 8

signed main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);
	string s = "OLQGA";
	sort (all (s));
	int ans = 0;
	do {
		int f = 1;
		if (s.front () == 'Q') f = 0;
		else {
			fl (i, 1, sz (s)) {
				if (s[i] == 'Q') {
					if (s[i - 1] == 'O' || s[i - 1] == 'A') f = 0;
				}
			}
		}
		ans += f;
	} while (next_permutation (all (s)));
	dbg (ans);
}

task 14

x = 343 ** 5 + 343 ** 4 + 49 ** 6 - 7 ** 13 - 21
a = set ()
while (x > 0):
	a.add (x % 7)
	x //= 7
# print (a)
print (len (a))

task 15

int check (int a, int x, int y) {
	int b = y > a;
	int c = x > a;
	int d = x * y < 120;
	return b || c || d;
}

signed main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);
	for (int a = 10000; a >= 0; --a) {
		int f = 1;
		fr (x, 1000) fr (y, 1000) f &= check (a, x, y);
		if (f) {
			dbg (a);
			exit (0);
		}
	}
}

task 16

int g(int);

int f (int n) {
	if (n == 1) return 1;
	return 2 * f (n - 1) - g (n - 1);
}

int g (int n) {
	if (n == 1) return 1;
	return f (n - 1) + 2 * g (n - 1);
}

signed main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);
	dbg (g (25) + f (25));

}

task 17

signed main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);
	int cnt = 0, mx = 0;
	fl (i, 100, 10000 + 1) {
		if (i % 10 == 3) {
			if (i % 8 == 7) {
				vector<int> a{13, 16, 19};
				int f = 1;
				for (auto& x: a) if (i % x == 0) f = 0;
				if (f && i % 21 == 0) {
					++cnt;
					mx = i;
				}
			}
		}
	}
	dbg (cnt);
	dbg (mx);
}

task 18

const int n = 12;

array <array <int, n>, n> goo, dp1, dp2;

signed main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);
	for (auto& v: goo) for (auto& x: v) cin >> x;

	fr (i, n) fr (j, n) {
		int mx = 0, mn = 1e9;
		if (goo[i][j] > 100) {
			dp1[i][j] = -1e18;
			dp2[i][j] = 1e18;
			continue;
		}
		if (i > 0) {
			mx = max (mx, dp1[i - 1][j]);
			mn = min (mn, dp2[i - 1][j]);
		}
		if (j > 0) {
			mx = max (mx, dp1[i][j - 1]);
			mn = min (mn, dp2[i][j - 1]);
		}
		dp1[i][j] = mx + goo[i][j], dp2[i][j] = mn + goo[i][j];
		if (mn == 1e9) dp1[i][j] = dp2[i][j] = goo[i][j];
	}
	cout << dp1[n - 1][n - 1] << ' ' << dp2[n - 1][n - 1] << '\n';
}

task 20

array <array <int, 100>, 100> dp;

vector<pair<int, int>> gen (int a, int b) {
	return {{a + 1, b}, {a * 2, b}, {a, b + 1}, {a, b * 2}};
}

int calc (int a, int b) {
	if (a + b >= 39) return 0;
	if (dp[a][b] != -1) return dp[a][b];
	auto t = gen (a, b);
	int cnt = 0;
	for (auto& x: t) cnt += calc (x.first, x.second);
	if (cnt == sz (t)) return dp[a][b] = 0;
	return dp[a][b] = 1;
}

signed main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);
	for (auto& v: dp) for (auto& x: v) x = -1;

	fl (i, 1, 30) {
		if (calc (i, 9)) {
			auto t = gen (i, 9);
			int f = 0;
			for (auto& x: t) {
				if (x.first + x.second >= 39) f = 1;
			}
			if (!f) {
				// dbg (make_pair (i, 9));
				f = 0;
				for (auto& x: t) {
					if (calc (x.first, x.second)) continue;
					// dbg (x);
					int c = 0;
					auto tt = gen (x.first, x.second);
					for (auto& xx: tt) {
						// dbg (xx);
						int ff = 0;
						auto ttt = gen (xx.first, xx.second);
						for (auto& xxx: ttt) {
							if (xxx.first + xxx.second >= 39) ff = 1;
							// dbg (xxx);
						}
						c += ff;
					}
					if (c == sz (tt)) f = 1;
				}
				if (f) {
					cout << i << ' ';
				// 	exit (0);
				}
			}
		}
	}
}

task 21

array <array <int, 100>, 100> dp;

vector<pair<int, int>> gen (int a, int b) {
	return {{a + 1, b}, {a * 2, b}, {a, b + 1}, {a, b * 2}};
}

int calc (int a, int b) {
	if (a + b >= 39) return 0;
	if (dp[a][b] != -1) return dp[a][b];
	auto t = gen (a, b);
	int cnt = 0;
	for (auto& x: t) cnt += calc (x.first, x.second);
	if (cnt == sz (t)) return dp[a][b] = 0;
	return dp[a][b] = 1;
}

signed main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);
	for (auto& v: dp) for (auto& x: v) x = -1;

	fl (i, 1, 30) {
		if (!calc (i, 9)) {
			auto t = gen (i, 9);
			int cnt1 = 0, j = 0;
			vector<int> used (sz (t));
			for (auto& x: t) {
				int f = 0;
				auto tt = gen (x.first, x.second);
				for (auto& xx: tt) {
					if (xx.first + xx.second >= 39) f = 1;
				}
				cnt1 += f;
				used[j] = f;
				++j;
			}
			if (cnt1 > 0 && cnt1 < sz (t)) {
				j = 0;
				for (auto& x: t) {
					if (!used[j]) {
						int f = 0;
						auto tt = gen (x.first, x.second);
						for (auto& xx: tt) {
							if (calc (xx.first, xx.second)) continue;
							int c = 0;
							auto ttt = gen (xx.first, xx.second);
							for (auto& xxx: ttt) {
								int ff = 0;
								auto tttt = gen (xxx.first, xxx.second);
								for (auto& xxxx: tttt) {
									if (xxxx.first + xxxx.second >= 39) ff = 1;
								}
								c += ff;
							}
							if (c == sz (ttt)) f = 1;
						}
						cnt1 += f;
					}
					++j;
				}
				if (cnt1 == sz (t)) cout << i << ' ';
			}
		}
	}
}

task 22

int kek (int x) {
	int a = 0, b = 0;
	while (x > 0) {
		a += x % 8;
		++b;
		x /= 8;
	}
	return a * b;
}

signed main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);
	fl (i, 1, 1000) {
		if (kek (i) == 20) {
			dbg (i);
			exit (0);
		}
	}
}

task 23

array<int, 100> dp;

signed main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);
	dp[1] = 1;
	fl (i, 1, 31) {
		if (i < 14) {
			if (i + 2 <= 14) dp[i + 2] += dp[i];
			if (i * 2 <= 14) dp[i * 2] += dp[i];
		} else {
			dp[i + 2] += dp[i];
			dp[i * 2] += dp[i];
		}
	}
	dbg (dp[30]);
}

task 24

signed main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);
	vector<string> goo;
	for (string s; cin >> s; ) goo.pb (s);
	int mn = 1e9;
	int pos = -1;
	fr (i, sz (goo)) {
		int cnt = 0;
		for (auto& x: goo[i]) cnt += x == 'A';
		if (cnt < mn) {
			mn = cnt;
			pos = i;
		}
	}
	map <char, int> cnt;
	for (auto& x: goo[pos]) ++cnt[x];
	int mx = 0;
	char kek;
	for (auto& x: cnt) {
		if (x.second >= mx) {
			mx = x.second;
			kek = x.first;
		}
	}
	cout << kek << ' ';
	int c = 0;
	for (auto& s: goo) for (auto& x: s) c += x == kek;
	cout << c << '\n';
}

task 25

signed main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);
	int cnt = 0;
	int mx = 0;
	int kek = 0;
	fl (a, 1, 5000 + 1) {
		fl (b, a, 5000 + 1) {
			int c = a * a + b * b;
			int c_kek = sqrt(c);
			if (c_kek * c_kek == c && c_kek <= 5000) {
				++cnt;
				if (a + b + c_kek > mx) {
					mx = a + b + c_kek;
					kek = c_kek;
				}
				cerr << a << ' ' << b << ' ' << c_kek << '\n';
			}
		}
	}
	cout << cnt << ' ' << kek << '\n';
}

task 26

signed main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);
	int n;
	cin >> n;
	vector<int> goo (n);
	for (auto& x: goo) cin >> x;
	unordered_set<int> kek;
	for (auto& x: goo) kek.insert (x);
	int cnt = 0, mx = 0;
	fr (i, n) {
		if (goo[i] % 2 == 0) continue;
		fl (j, i + 1, n) {
			if (goo[j] % 2 == 0) continue;
			if (kek.count ((goo[i] + goo[j]) / 2)) {
				++cnt;
				mx = max (mx, (goo[i] + goo[j]) / 2);
			}
		}
	}
	cout << cnt << ' ' << mx << '\n';
}

task 27

signed main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);
	int n;
	cin >> n;
	vector<int> goo (n);
	for (auto& x: goo) cin >> x;
	vector<int> mx1 (80), mx2 (80);
	for (auto& x: goo) {
		if (x > mx1[x % 80]) {
			mx2[x % 80] = mx1[x % 80];
			mx1[x % 80] = x;
		} else if (x > mx2[x % 80]) {
			mx2[x % 80] = x;
		}
	}
	int mx = 0;
	fr (i, 80) {
		if (mx2[i] > 0) mx = max (mx, mx1[i] + mx2[i]);
	}
	cout << mx << '\n';
}