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;

//ABC046-C-AtCoDeerくんと選挙速報
//http://abc046.contest.atcoder.jp/tasks/arc062_a
class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("3");
            WillReturn.Add("2 3");
            WillReturn.Add("1 1");
            WillReturn.Add("3 2");
            //10
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("4");
            WillReturn.Add("1 1");
            WillReturn.Add("1 1");
            WillReturn.Add("1 5");
            WillReturn.Add("1 100");
            //101
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("5");
            WillReturn.Add("3 10");
            WillReturn.Add("48 17");
            WillReturn.Add("31 199");
            WillReturn.Add("231 23");
            WillReturn.Add("3 2");
            //6930
        }
        //else if (InputPattern == "Input4") {
        //    WillReturn.Add("5");
        //    WillReturn.Add("3 11");
        //    WillReturn.Add("11 3");
        //    WillReturn.Add("3 11");
        //    WillReturn.Add("11 3");
        //    WillReturn.Add("1 1");
        //}
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        //Console.WriteLine(DeriveMinBaisuu(11, 3));
        //return;

        List<string> InputList = GetInputList();

        long[] wkArr = { };
        Action<string> SplitAct = pStr =>
            wkArr = pStr.Split(' ').Select(X => long.Parse(X)).ToArray();

        long TotalT = 1;
        long TotalA = 1;

        foreach (string EachStr in InputList.Skip(1)) {
            SplitAct(EachStr);
            long CurrT = wkArr[0];
            long CurrA = wkArr[1];

            //TotalT以上で最小のCurrTの倍数を求める
            long MinBaisuuT = DeriveMinBaisuu(TotalT, CurrT);

            //TotalA以上で最小のCurrAの倍数を求める
            long MinBaisuuA = DeriveMinBaisuu(TotalA, CurrA);

            //倍率を求める
            long BairituT = MinBaisuuT / CurrT;
            long BairituA = MinBaisuuA / CurrA;

            //大きいほうの倍率となる
            long Bairitu = Math.Max(BairituT, BairituA);

            TotalT = CurrT * Bairitu;
            TotalA = CurrA * Bairitu;

            //Console.WriteLine("CurrT={0},CurrA={1},TotalT={2},TotalA={3}",
            //    CurrT, CurrA, TotalT, TotalA);
        }
        Console.WriteLine(TotalT + TotalA);
    }

    //A,Bを引数として、A以上で最小のBの倍数を求める
    static long DeriveMinBaisuu(long pA, long pB)
    {
        long Syou = pA / pB;
        long Amari = pA % pB;

        return pB * (Syou + Math.Sign(Amari));
    }
}