#!/bin/python3 import sys def gcd(a, b): while (b != 0): remainder = a % b a = b b = remainder return a def Pollard(n, primes, known_primes): if n == 1: return 1 if n in primes: return n for p in known_primes: if p*p > n: return n elif n%p == 0: return p x = 2 + sys.hexversion % n y = x d = 1 while d == 1: x = (x*x+1)%n y = (y*y+1)%n y = (y*y+1)%n d = gcd(abs(x - y), n) if d == n: d = int((n**0.5)) if d*d == n: return d else: return n else: return d def findAllFactors(N, primes, known_primes): factors = [N] # queue prime_factors = [] while len(factors)>0: cur = factors.pop() fcur = Pollard(cur, primes, known_primes) if cur == fcur: # prime prime_factors.append(cur) primes.add(cur) else: factors.append(fcur) factors.append(int(cur/fcur)) return prime_factors def findMoves(N, cheatsheet): """ Args: N: the number e.g. 24 factors: sorted prime factors of number N e.g. [1,2,2,2,3] cheatsheet: a dict of N:findMoves() e.g. {24:46, 8:15, ...} """ known_primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997] primes = set(known_primes) factors = findAllFactors(N, primes, known_primes) factors.append(1) factors.sort() n = N i = len(factors)-1 while cheatsheet.get(n) == None and i>0: n = int(n/factors[i]) i -= 1 res = cheatsheet.get(n) while i < len(factors)-1: i += 1 n = n*factors[i] res = 1 + res * factors[i] cheatsheet[n] = res ##print(factors, cheatsheet, res, n) return res def longestSequence(a): # Return the length of the longest possible sequence of moves. cheatsheet = {1:1} res = 0 for n in a: if n == 1: res += 1 else: res += findMoves(n, cheatsheet) return res if __name__ == "__main__": n = int(input().strip()) a = list(map(int, input().strip().split(' '))) result = longestSequence(a) print(result)