Problem:
Score : 200 points

Problem Statement

Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.

The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)

Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?

Constraints

101 \le X \le 10^{18}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X

Output

Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.

Sample Input 1

103

Sample Output 1

3

The balance after one year is 101 yen.

The balance after two years is 102 yen.

The balance after three years is 103 yen.

Thus, it takes three years for the balance to reach 103 yen or above.

Sample Input 2

1000000000000000000

Sample Output 2

3760

Sample Input 3

1333333333

Sample Output 3

1706

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using System.IO;

namespace AtCoder
{
	class Program
	{
		public static void Main()
		{
#if TextInput
			using(var reader = new StreamReader(Debug.SampleTextPath)) 
			{
				Console.SetIn(reader);
#endif
				var money = IO.ReadLong();
				var currentMoney = 100L;
				var year = 1L;
				while(true)
				{
					currentMoney = currentMoney + (long)(currentMoney * 0.01);
					if(currentMoney >= money) { break; }
					++ year;
				}
				IO.Write(year);
#if TextInput
			}
#endif
		}

		
	}

	public static class IO
	{
		public static string   Read()								 { return Console.ReadLine(); }
		public static string[] ReadArray(char iSplitter = ' ')		 { return Read().Split(iSplitter); }
		public static int	   ReadInt()							 { return int.Parse(Read()); }
		public static int[]	   ReadIntArray(char iSplitter = ' ')	 { return ReadArray().Select(iText => int.Parse(iText)).ToArray(); }
		public static long	   ReadLong()							 { return long.Parse(Read()); }
		public static long[]   ReadLongArray(char iSplitter = ' ')	 { return ReadArray().Select(iText => long.Parse(iText)).ToArray(); }
		public static double   ReadDouble()							 { return double.Parse(Read()); }
		public static double[] ReadDoubleArray(char iSplitter = ' ') { return ReadArray().Select(iText => double.Parse(iText)).ToArray(); }
		public static char[]   ReadCharArray()						 { return Read().ToCharArray(); }

		public static void Write(string iValue)	 { Console.WriteLine(iValue); }
		public static void Write(int iValue)	 { Console.WriteLine(iValue); }
		public static void Write(long iValue)	 { Console.WriteLine(iValue); }
		public static void Write(double iValue)  { Console.WriteLine(iValue); }
		public static void Write(decimal iValue) { Console.WriteLine(iValue); }
		public static void Write(bool iValue)	 { Console.WriteLine(iValue ? "Yes" : "No"); }
		public static void Write<Type>(IEnumerable<Type> iValue , string iJoinWord = " ") { Console.WriteLine(string.Join(iJoinWord , iValue)); }
	}

	public static class Util
	{
		public static long Gcd(long i0 , long i1) { return (i0 > i1) ? _Gcd(i0 , i1) : _Gcd(i1 , i0); }
		public static long Lcm(long i0 , long i1) { return (i0 * i1) / Gcd(i0 , i1); }
		public static long ModPow(long iBaseNumber , long iPow , long iModNumber)
		{
			var num = 1L;
			while(iPow != 0)
			{
				if((iPow & 0x1) != 0)
				{
					num = (num * iBaseNumber) % iModNumber;
				}
				iBaseNumber = (iBaseNumber * iBaseNumber) % iModNumber;
				iPow >>= 1;
			}
			return num;
		}
		public static long CombinationNum(int iLeftNumber , int iRightNumber)
		{
			if(iRightNumber == 0) { return 1; }
			if(iLeftNumber == 0)  { return 0; }
			return iLeftNumber * CombinationNum(iLeftNumber - 1 , iRightNumber - 1) / iRightNumber;
		}
		public static long Factorial(long iNumber)
		{
			if(iNumber == 0) { return 1L; }
			return iNumber * Factorial(iNumber - 1);
		}
		private static long _Gcd(long i0 , long i1)	{ return (i1 == 0) ? i0 : _Gcd(i1 , i0 % i1); }
	}

	public class UnionFind
	{
		public int[] Parents;
		public int[] RootNums;
		public UnionFind(int iRootNum)
		{
			Parents = Enumerable.Range(0 , iRootNum).ToArray();
			RootNums = new int[iRootNum];
		}
		public void Normalize()
		{
			for(var iIndex = 0 ; iIndex < Parents.Length ; ++ iIndex)
			{
				var rootIndex = _GetRoot(iIndex);
				++ RootNums[rootIndex];
				Parents[iIndex] = rootIndex;
			}
		}
		public void Union(int iNumber0 , int iNumber1)
		{
			var rootNumber0 = _GetRoot(iNumber0);
			var rootNumber1 = _GetRoot(iNumber1);
			if(rootNumber0 < rootNumber1)
			{
				Parents[rootNumber1] = rootNumber0;
			}
			else
			{
				Parents[rootNumber0] = rootNumber1;
			}
		}
		public int _GetRoot(int iNumber)
		{
			return (Parents[iNumber] == iNumber) ? iNumber : _GetRoot(Parents[iNumber]);
		}
	}

	public class CumulativeSum
	{
		public static CumulativeSum Create(IEnumerable<long> iNumbers)
		{
			var numbers = iNumbers.ToArray();
			var cumulativeSum = new CumulativeSum
			{
				Numbers = numbers,
				SumNumbers = new long[numbers.Length + 1]
			};
			var sumNumber = 0L;
			for(var iIndex = 0 ; iIndex < numbers.Length ; ++ iIndex)
			{
				sumNumber += numbers[iIndex];
				cumulativeSum.SumNumbers[iIndex + 1] = sumNumber;
			}
			return cumulativeSum;
		}

		public long[] Numbers { get; private set; }
		public long[] SumNumbers { get; private set; }

		public int GetMaxTotalIndex(int iAreaNum)
		{
			var maxIndex = -1;
			var maxNumber = 0L;
			var num = Numbers.Length - iAreaNum + 1;
			for(var iIndex = 0 ; iIndex < num ; ++ iIndex)
			{
				var checkNumber = SumNumbers[iAreaNum + iIndex] - SumNumbers[iIndex];
				if(maxNumber < checkNumber) 
				{
					maxIndex = iIndex;
					maxNumber = checkNumber;
				}
			}
			return maxIndex;
		}
	}
}