Bamboo Pole-vault is a massively popular sport in Xzhiland. And Master Phi-shoe is a very popular coach for his success. He needs some bamboos for his students, so he asked his assistant Bi-Shoe to go to the market and buy them. Plenty of Bamboos of all possible integer lengths (yes!) are available in the market. According to Xzhila tradition,
Score of a bamboo = Φ (bamboo’s length)
(Xzhilans are really fond of number theory). For your information, Φ (n) = numbers less than n which are relatively prime (having no common divisor other than 1) to n. So, score of a bamboo of length 9 is 6 as 1, 2, 4, 5, 7, 8 are relatively prime to 9.
The assistant Bi-shoe has to buy one bamboo for each student. As a twist, each pole-vault student of Phi-shoe has a lucky number. Bi-shoe wants to buy bamboos such that each of them gets a bamboo with a score greater than or equal to his/her lucky number. Bi-shoe wants to minimize the total amount of money spent for buying the bamboos. One unit of bamboo costs 1 Xukha. Help him.
例如:给定的数字为 2, 我们知道phi2 = 1, phi = 2,phi = 2….;
我们可以发现，phi和phi 都是等于2，满足phi >= 2 ，而且值也是 > 2，所以这时候3,4都是满足题意的，但是k最小，所以我们只能取3；
由于欧拉函数的性质，phi[p] = p - 1, 当p是素数的时候； 当给出的数字不是素数时 ，这时候的phi一定会 < 给出的值的； 所以，我们只需要找到比这个数大的最小的质数，然后累加输出答案即可；
PS：累加的过程会爆int，开long long 可以过;