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: Accepted)

import java.util.*;
import java.io.*;

public class Main {
	public static void main(String[] args) {
		FastScanner br = new FastScanner();
		PrintWriter pw = new PrintWriter(new OutputStreamWriter(System.out));
		int n1 = br.ni();
		long l1 = 1;
		long l2 = 1;
		for(int i = 0;i<n1;i++) {
			long j1 = br.ni();
			long j2 = br.ni();
			long n = Math.max((l1+j1-1)/j1, (l2+j2-1)/j2);

			l1=j1*n;
			l2=j2*n;
		}
		pw.println(l1+l2);
		pw.close();
	}
}

class FastScanner {
	BufferedReader br;
	StringTokenizer st;

	public FastScanner(String s) {
		try {
			br = new BufferedReader(new FileReader(s));
		} catch (FileNotFoundException e) {
			e.printStackTrace();
		}
	}

	public FastScanner() {
		br = new BufferedReader(new InputStreamReader(System.in));
	}

	ArrayList<Integer>[] ng(int n, int e) {
		ArrayList<Integer>[] adj = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			adj[i] = new ArrayList<Integer>();
		}
		for (int i = 0; i < e; i++) {
			int a = ni() - 1;
			int b = ni() - 1;
			adj[a].add(b);
			adj[b].add(a);
		}
		return adj;
	}

	Integer[] nIa(int n) {
		Integer[] arr = new Integer[n];
		for (int i = 0; i < n; i++) {
			arr[i] = ni();
		}
		return arr;
	}

	int[] nia(int n) {
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = ni();
		}
		return arr;
	}

	Long[] nLa(int n) {
		Long[] arr = new Long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nl();
		}
		return arr;
	}

	long[] nla(int n) {
		long[] arr = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nl();
		}
		return arr;
	}

	String[] nsa(int n) {
		String[] arr = new String[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nt();
		}
		return arr;
	}

	String nt() {
		while (st == null || !st.hasMoreElements()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				e.printStackTrace();
			}
		}
		return st.nextToken();
	}

	int ni() {
		return Integer.parseInt(nt());
	}

	long nl() {
		return Long.parseLong(nt());
	}

	double nd() {
		return Double.parseDouble(nt());
	}

}