Problem:
Score : 300 points

Problem Statement

AtCoDeer the deer is seeing a quick report of election results on TV.
Two candidates are standing for the election: Takahashi and Aoki.
The report shows the ratio of the current numbers of votes the two candidates have obtained, but not the actual numbers of votes.
AtCoDeer has checked the report N times, and when he checked it for the i-th (1≦i≦N) time, the ratio was T_i:A_i.
It is known that each candidate had at least one vote when he checked the report for the first time.

Find the minimum possible total number of votes obtained by the two candidates when he checked the report for the N-th time.
It can be assumed that the number of votes obtained by each candidate never decreases.

Constraints

1≦N≦1000

1≦T_i,A_i≦1000 (1≦i≦N)

T_i and A_i (1≦i≦N) are coprime.

It is guaranteed that the correct answer is at most 10^{18}.

Input

The input is given from Standard Input in the following format:

N
T_1 A_1
T_2 A_2
:
T_N A_N

Output

Print the minimum possible total number of votes obtained by Takahashi and Aoki when AtCoDeer checked the report for the N-th time.

Sample Input 1

3
2 3
1 1
3 2

Sample Output 1

10

When the numbers of votes obtained by the two candidates change as 2,3 → 3,3 → 6,4, the total number of votes at the end is 10, which is the minimum possible number.

Sample Input 2

4
1 1
1 1
1 5
1 100

Sample Output 2

101

It is possible that neither candidate obtained a vote between the moment when he checked the report, and the moment when he checked it for the next time.

Sample Input 3

5
3 10
48 17
31 199
231 23
3 2

Sample Output 3

6930

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

/*
 * シカのAtCoDeerくんは選挙速報を見ています。選挙には二人の候補高橋くんと青木くんが出ています。速報では、現在の二人の得票数の比が表示されていますが、得票数そのものは表示されていません。
 * AtCoDeerくんは N 回画面を見て、 i(1≦i≦N) 回目に見たときに表示されている比は Ti:Ai でした。
 * ここで、AtCoDeerくんが選挙速報の画面を1回目に見た段階で既にどちらの候補にも少なくとも一票は入っていたことがわかっています。
 * N 回目に画面を見たときの投票数(二人の得票数の和)として考えられるもののうち最小となるものを求めてください。ただし、得票数が途中で減ることはありません。
 */

import java.util.*;
	public class Main{
		public static void main(String[] args){
            Scanner sc = new Scanner(System.in);
            //入力
            int n = Integer.parseInt(sc.next());
            
            long t = 1;
            long a = 1;
            
            // 
            for(int i=0; i<n; i++){
            	// 
            	int ti = Integer.parseInt(sc.next());
                int ai = Integer.parseInt(sc.next());
                long temp = (long)Math.max(Math.ceil(t*1.0/ti), Math.ceil(a*1.0/ai));
                t = temp * ti;
                a = temp * ai;
            }
            
            System.out.println(t + a);
            sc.close();
		}
    }