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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;

namespace kyoupuro {

    class MainClass {

        public static void Main() {
            var N = Input.NextInt();
            long taka = Input.NextLong();
            long aoki = Input.NextLong();
            double rate = (double)taka / aoki;

            for (int i = 1; i < N; i++) {
                long ttmp = Input.NextLong();
                long atmp = Input.NextLong();
                double ratetmp = (double)ttmp / atmp;

                // takahashiを中心に上昇
                if(rate < ratetmp) {
                    // aokiの設定
                    aoki = ((aoki - 1) / atmp + 1) * atmp;
                    // takahashiの設定
                    taka = (aoki / atmp) * ttmp;
                }

                // aokiを中心に上昇
                if(rate > ratetmp) {
                    taka = ((taka - 1) / ttmp + 1) * ttmp;
                    aoki = (taka / ttmp) * atmp;
                }

                rate = ratetmp;
            }

            Console.WriteLine(taka + aoki);
        }
    }

    class Input {
        static IEnumerator<string> enumerator;

        public static string Line() {
            return Console.ReadLine();
        }

        public static int NextInt() {
            if (enumerator == null || !enumerator.MoveNext()) {
                enumerator = StrArr().AsEnumerable().GetEnumerator();
                enumerator.MoveNext();
            }
            return int.Parse(enumerator.Current);
        }

        public static long NextLong() {
            if (enumerator == null || !enumerator.MoveNext()) {
                enumerator = StrArr().AsEnumerable().GetEnumerator();
                enumerator.MoveNext();
            }
            return long.Parse(enumerator.Current);
        }

        public static string[] StrArr() {
            return Line().Split(' ');
        }

        public static List<int> IntList() {
            return StrArr().Select(int.Parse).ToList();
        }

        public static List<long> LongList() {
            return StrArr().Select(long.Parse).ToList();
        }

        public static void Skip(int line = 1) {
            enumerator.Reset();
            for (int i = 0; i < line; i++) Console.ReadLine();
        }

        public static void Reset() {
            enumerator.Reset();
        }
    }
}