Bi-shoe and Phi-shoe LightOJ

Bi-shoe and Phi-shoe

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.

Input

Input starts with an integer T (≤ 100), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n ≤ 10000) denoting the number of students of Phi-shoe. The next line contains n space separated integers denoting the lucky numbers for the students. Each lucky number will lie in the range [1, 10⁶].

Output

For each case, print the case number and the minimum possible money spent for buying the bamboos. See the samples for details.

Sample Input

3

5

1 2 3 4 5

6

10 11 12 13 14 15

2

1 1

Sample Output

Case 1: 22 Xukha

Case 2: 88 Xukha

Case 3: 4 Xukha

题意：

给出 n 个数字的序列 a[n] , 对于每个数字ai 找到一个数字 bi 使得 bi的欧拉函数值大于等于 a ，求满足条件的 bi 的和的最小值sum.

思路：欧拉函数打表后对于每个a 从 a+1 开始遍历，寻找满足条件的最小的b求和即可。

代码:

#include <set>
#include <map>
#include <list>
#include <stack>
#include <queue>
#include <deque>
#include <cmath>
#include <string>
#include <vector>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <sstream>
#include <iostream>
#include <algorithm>
#include <unordered_map>
#define INF 0x3f3f3f3f
#define ll long long
#define ull unsigned long long
#define fcio ios::sync_with_stdio(false); cin.tie(0); cout.tie(0)
using namespace std;
const int maxn=1e6+10;
int euler[maxn];
void dbeuler(void)
{
    for(int i=0;i<maxn;i++) euler[i]=i;
    for(int i=2;i<maxn;i++)
    {
        if(euler[i]==i)
        {
            for(int j=i;j<maxn;j+=i) euler[j]=euler[j]/i*(i-1);
        }
    }
}

int main()
{
    dbeuler();
    int n;
    int t;
    cin>>t;
    for(int k=1;k<=t;k++)
    {
        cin>>n;
        ll sum=0;
        for(int i=0;i<n;i++)
        {
            int a;
            cin>>a;
            for(int j=a+1;j<maxn;j++)
            {
                if(euler[j]>=a)
                {
                    sum+=j;
                    break;
                }
            }
        }
        cout<<"Case "<<k<<": "<<sum<<" Xukha"<<endl;
    }
}