## https://yukicoder.me/problems/no/1694 from collections import deque def main(): N = int(input()) A = list(map(int, input().split())) # osa-k法により素因数分解を実施 max_a = max(A) min_primes = [i for i in range(max_a + 1)] for p in range(2, max_a + 1): if p != min_primes[p]: continue x = 2 * p while x <= max_a: if min_primes[x] == x: min_primes[x] = p x += p prime_divisors = [[] for _ in range(max_a +1)] for a0 in range(2, max_a + 1): a = a0 primes = set() while min_primes[a] != a: p = min_primes[a] primes.add(p) a //= p if a > 1: primes.add(a) prime_divisors[a0] = primes # 各i について「連結成分」を計算し、最小の数字を記録 exists_a = [[] for _ in range(max_a + 1)] for i in range(N): a = A[i] exists_a[a].append(i) composite_id_list = [-1] * N composite_primes = {} composite_id = 0 for i in range(N): if composite_id_list[i] == -1: queue = deque() queue.append((i, 0)) composite_id_list[i] = composite_id while len(queue) > 0: v, typ = queue.popleft() if typ == 1: a = v else: a = A[v] if a == 1: continue if typ == 1: x = a while x <= max_a: for w in exists_a[x]: if composite_id_list[w] == -1: composite_id_list[w] = composite_id queue.append((w, 0)) x += a else: # typ == 0: for p in prime_divisors[a]: if p not in composite_primes: composite_primes[p] = composite_id queue.append((p, 1)) composite_id += 1 # 連結成分に所属する数字の中での最小値を計算する composite_id_map = {} for i in range(N): c_id = composite_id_list[i] if c_id not in composite_id_map: composite_id_map[c_id] = max_a for d in prime_divisors[A[i]]: composite_id_map[c_id] = min(composite_id_map[c_id], d) # 連結になるように対処する if len(composite_id_map) == 1: print(0) else: min_answer = float("inf") for c_id0, a in composite_id_map.items(): if a == 1: continue ans = a * (len(composite_id_map) - 1) min_answer = min(min_answer, ans) print(min_answer) # どこかの連結成分に合わせるということをする if __name__ == "__main__": main()