Codeforces 923A - Primal Sport

전송문:Primal Sport
A. Primal Sport
time limit per test
1.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Alice and Bob begin their day with a quick game. They first choose a starting number X0 ≥ 3 and try to reach one million by the process described below.
Alice goes first and then they take alternating turns. In the i-th turn, the player whose turn it is selects a prime number smaller than the current number, and announces the smallest multiple of this prime number that is not smaller than the current number.
Formally, he or she selects a prime p Xi - 1 and then finds the minimum Xi ≥ Xi - 1 such that p divides Xi. Note that if the selected prime palready divides Xi - 1, then the number does not change.
Eve has witnessed the state of the game after two turns. Given X2, help her determine what is the smallest possible starting number X0. Note that the players don't necessarily play optimally. You should consider all possible game evolutions.
Input
The input contains a single integer X2 (4 ≤ X2 ≤ 106). It is guaranteed that the integer X2 is composite, that is, is not prime.
Output
Output a single integer — the minimum possible X0.
Examples
input
Copy

14

output

6

input
Copy

20

output

15

input
Copy

8192

output

8191

Note
In the first test, the smallest possible starting number is X0 = 6. One possible course of the game is as follows:
Alice picks prime 5 and announces X1 = 10
Bob picks prime 7 and announces X2 = 14.
In the second case, let X0 = 15.
Alice picks prime 2 and announces X1 = 16
Bob picks prime 5 and announces X2 = 20.
분석: f(n)를 설정하면 N의 최대 질량 계수를 나타냅니다.
그러면 X2를 분해한 후에 X1의 수치 범위는 [X2-P(X2)+1, X2]이고 X0의 수치는 [X1-P(X1)+1, X1]이다.
시간 복잡도 O(N*sqrt(N))
Bonus: Q개 쿼리 Xk, 시간 복잡도 O (N log N + Q log K)
코드는 다음과 같습니다.

#include 
using namespace std;

const int maxn = 1e6+10;
int n,ans;
int f[maxn];

inline int Min(int x, int y) {return x