# input import sys # input = sys.stdin.readline II = lambda : int(input()) MI = lambda : map(int, input().split()) LI = lambda : [int(a) for a in input().split()] SI = lambda : input().rstrip() LLI = lambda n : [[int(a) for a in input().split()] for _ in range(n)] LSI = lambda n : [input().rstrip() for _ in range(n)] MI_1 = lambda : map(lambda x:int(x)-1, input().split()) LI_1 = lambda : [int(a)-1 for a in input().split()] mod = 998244353 inf = 1001001001001001001 ordalp = lambda s : ord(s)-65 if s.isupper() else ord(s)-97 ordallalp = lambda s : ord(s)-39 if s.isupper() else ord(s)-97 yes = lambda : print("Yes") no = lambda : print("No") yn = lambda flag : print("Yes" if flag else "No") prinf = lambda ans : print(ans if ans < 1000001001001001001 else -1) alplow = "abcdefghijklmnopqrstuvwxyz" alpup = "ABCDEFGHIJKLMNOPQRSTUVWXYZ" alpall = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ" URDL = {'U':(-1,0), 'R':(0,1), 'D':(1,0), 'L':(0,-1)} DIR_4 = [[-1,0],[0,1],[1,0],[0,-1]] DIR_8 = [[-1,0],[-1,1],[0,1],[1,1],[1,0],[1,-1],[0,-1],[-1,-1]] DIR_BISHOP = [[-1,1],[1,1],[1,-1],[-1,-1]] prime60 = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59] sys.set_int_max_str_digits(0) # sys.setrecursionlimit(10**6) # import pypyjit # pypyjit.set_param('max_unroll_recursion=-1') from collections import defaultdict,deque from heapq import heappop,heappush from bisect import bisect_left,bisect_right DD = defaultdict BSL = bisect_left BSR = bisect_right from math import isqrt from random import randint def gcd(x, y): """ x < y """ while y: x, y = y, x%y return x def is_prime(num): """ 1 <= x < 1<<64 """ if num < 4: return num > 1 if not num&1: return False d, s = num-1, 0 while not d&1: d >>= 1 s += 1 tests = (2,7,61) if num < 4759123141 else (2,325,9375,28178,450775,9780504,1795265022) for test in tests: if test >= num: return True t = pow(test, d, num) if 1 < t < num-1: for _ in range(s-1): t = t*t%num if t == num-1: break else: return False return True def find_prime(n): b = n.bit_length() - 1 b = (b >> 2) << 2 m = (1 << (b >> 3)) << 1 while True: c = randint(1, n - 1) y = 0 g = q = r = 1 while g == 1: x = y for _ in range(r): y = (y * y + c) % n k = 0 while k < r and g == 1: ys = y for _ in range(min(m, r - k)): y = (y * y + c) % n q = q * abs(x - y) % n g = gcd(q, n) k += m r <<= 1 if g == n: g = 1 y = ys while g == 1: y = (y * y + c) % n g = gcd(abs(x - y), n) if g == n: continue if is_prime(g): return g elif is_prime(n // g): return n // g else: n = g def _primefactor(n): result = [] for p in range(2, 500): if p * p > n: break c = 0 while n%p == 0: n //= p c += 1 if c: result.append(p) while n > 1 and not is_prime(n): p = find_prime(n) while n % p == 0: n //= p result.append(p) if n > 1: result.append(n) return result def primefact(n, deduplicate = True): if deduplicate == False: return _primefactor(n) result = dict() for p in range(2, 500): if p * p > n: break c = 0 while n%p == 0: n //= p c += 1 if c: result[p] = c while n > 1 and not is_prime(n): p = find_prime(n) c = 0 while n % p == 0: n //= p c += 1 result[p] = c if n > 1: result[n] = 1 return result def divisors_naive(n): divs_small, divs_big = [], [] i = 1 while i*i <= n: if n % i == 0: divs_small.append(i) if i != n//i: divs_big.append(n//i) i += 1 return divs_small + divs_big[::-1] def divisors(n): if n == 1: return [1] if n <= 100_000_000: # 10 ** 8 return divisors_naive(n) pf = primefact(n) ps = list(pf.keys()) es = list(pf.values()) us = [p ** e for p,e in zip(ps, es)] l = len(es) nes = [0] * (l + 1) r = 1 res = [1] while True: nes[0] += 1 for i in range(l): if nes[i] > es[i]: if i+1 == l: res.sort() return res nes[i] = 0 nes[i+1] += 1 r //= us[i] else: r *= ps[i] break res.append(r) def totient(n): """ totient(n) = #{ m | (m,n) = 1, 1 <= m <= n } """ pf = _primefactor(n) for p in pf: n //= p n *= p - 1 return n def mobius(n): pf = primefact(n) r = 1 for p,e in pf.items(): if e >= 2: return 0 r *= -1 return r def primitive_root(p): """ p : prime """ if p == 2: return 1 r = p - 1 tests = [] for q in range(2, 500): if q * q > r: break if r % q == 0: while r % q == 0: r //= q tests.append((p - 1) // q) while r > 1 and not is_prime(r): q = find_prime(r) while r % q == 0: r //= q tests.append((p - 1) // q) if r > 1: tests.append((p - 1) // r) res = 2 while True: for test in tests: if pow(res, test, p) == 1: break else: return res res = randint(3, p - 2) """ つまり B 「ある i, j, k が一致するか?」のみ聞ける n <= 1e6 q = 1600 n ができればできる? - k を fai(n) にして聞けば ok - i = 0, j != 0 で 0 も回避可能 ということで n を特定する問題 そもそもおなじ x を期待するのってそんなに簡単なのか? 支配的な項は k とおもうべきかも 乱択かも? たとえば多くの N で 1 を返す関数を考える -> 約数がおおいとか? 誕生日攻撃とか? 1000 回でおよそ 4 割成功 -> カス 1600 で 7 割 --- 直接 N を返す関数を作るべきだなー たとえば i にめっちゃ約数が多い数を選ぶみたいな戦法もありうる --- それは k でやったほうが効率的 i と j が両方あるの何の意味があるんでしょう? たとえば偶数にできる -> ? --- BS-GS とかに寄せるべき? 乱択でまともにできる気がせん。 --- 適当な集合で x, y in S で (x - y) % N == 0 が存在すればよいという説 できそう できません。たすけて あー、サイズを半分にできるのか """ from random import randint # lim = 10 ** 6 # s = [] # ok = {0,} # # while len(ok) < lim + 1: # for _ in range(1400): # best = (-1, -1) # for _ in range(100): # x = randint(1, lim) # add = sum(1 for y in s if abs(x - y) not in ok) # best = max(best, (add, x)) # x = best[1] # for y in s: # ok.add(abs(x - y)) # s.append(x) # # print(len(ok), len(s)) b = 710 s = [*range(0, b)] + [5 * 10 ** 5 + b * i for i in range(b)] # print(len(s)) # print(s) t = II() for i in range(n): qc = 0 def ask(i, j, k): global qc qc += 1 print("?", i, j, k) return int(input()) k = 10 ** 6 + 33 cnt = DD(list) for x in s: cnt[ask(x, 0, k)].append(x) n = 0 for v, c in cnt.items(): c.sort() for i in range(len(c) - 1): n = gcd(n, c[j] - c[i]) # n を求めたあと phi = totient(n) phi = max(phi, 2) b = DD(int) while qc < 1600: i = randint(0, 10 ** 9) b[ask(i, 0, phi)] += 1 ans = max((v, k) for k, v in b.items())[1] print("!", ans)