Codeforces Round #132(Div2) A.Bicycle Chain

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本文介绍了一种算法，用于解决自行车变速器中齿轮比的计算问题。通过输入前后轮轴上的星形齿轮数量和各自齿数，算法找出所有整数齿轮比，并确定具有最大整数齿轮比的组合数量。

A. Bicycle Chain

time limit per test 2 seconds

time limit per test 1 second memory limit per test 256 megabytes input:standard input output:standard output

Vasya’s bicycle chain drive consists of two parts: n stars are attached to the pedal axle, m stars are attached to the rear wheel axle. The chain helps to rotate the rear wheel by transmitting the pedal rotation.

We know that the i-th star on the pedal axle has a_i (0 < a₁ < a₂ < … < a_n) teeth, and the j-th star on the rear wheel axle has b_j(0 < b₁ < b₂ < … < b_m) teeth. Any pair (i, j) (1 ≤ i ≤ n; 1 ≤ j ≤ m) is called a gear and sets the indexes of stars to which the chain is currently attached. Gear (i, j) has a gear ratio, equal to the value .

Since Vasya likes integers, he wants to find such gears (i, j), that their ratios are integers. On the other hand, Vasya likes fast driving, so among all “integer” gears (i, j) he wants to choose a gear with the maximum ratio. Help him to find the number of such gears.

In the problem, fraction denotes division in real numbers, that is, no rounding is performed.

Input

The first input line contains integer n (1 ≤ n ≤ 50) — the number of stars on the bicycle’s pedal axle. The second line contains n integers a₁, a₂, …, a_n (1 ≤ a_i ≤ 10⁴) in the order of strict increasing.

The third input line contains integer m (1 ≤ m ≤ 50) — the number of stars on the rear wheel axle. The fourth line contains m integers b₁, b₂, …, b_m (1 ≤ b_i ≤ 10⁴) in the order of strict increasing.

It is guaranteed that there exists at least one gear (i, j), that its gear ratio is an integer. The numbers on the lines are separated by spaces.

Output

Print the number of “integer” gears with the maximum ratio among all “integer” gears.

Examples

input

2
4 5
3
12 13 15

output

input

4
1 2 3 4
5
10 11 12 13 14

output

Note

In the first sample the maximum “integer” gear ratio equals 3. There are two gears that have such gear ratio. For one of them a₁ = 4, b₁ = 12, and for the other a₂ = 5, b₃ = 15.

题解

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <string>
#include <cstring>
#include <cmath>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <utility>
#define ll long long
#define ull_ unsigned long long

using namespace std ;

int main(){
    int a , b ;
    cin >> a ;
    int num_a[a + 10] ;
    for ( int i = 0 ; i < a ; i ++ ){
        cin >> num_a[i] ;
    }
    cin >> b ;
    int num_b[b + 10] ;
    for ( int i = 0 ; i < b ; i ++ ){
        cin >> num_b[i] ;
    }
    int ans = 0 ;
    int maxx = -1 ;
    for ( int i = 0 ; i < a ; i ++ ){
        for ( int j = 0 ; j < b ; j ++ ){
            if ( num_b[j] % num_a[i] == 0 ){
                maxx = max(maxx , num_b[j] / num_a[i]) ;
            }
        }
    }
    for ( int i = 0 ; i < a ; i ++ ){
        for ( int j = 0 ; j < b ; j ++ ){
            if ( num_b[j] % num_a[i] == 0 && num_b[j] / num_a[i] == maxx ){
                ans ++ ;
            }
        }
    }
    cout << ans << endl ;
    return 0 ;
}