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# (Mono-mcs 6.8.0.105) (judge verdict: Accepted)

/*******************************************************************************
* Author: Nirushuu
*******************************************************************************/

using System;
using System.Collections.Generic;
using System.Linq;
using System.Windows;
using System.IO;
using System.Globalization;
using System.Numerics;

/*******************************************************************************
* IO from Kattio.cs from open.kattis.com/help/csharp                          */
public class NoMoreTokensException : Exception
{
}

public class Tokenizer
{
    string[] tokens = new string[0];
    private int pos;
    StreamReader reader;

    public Tokenizer(Stream inStream)
    {
        var bs = new BufferedStream(inStream);
        reader = new StreamReader(bs);
    }

    public Tokenizer() : this(Console.OpenStandardInput())
    {
        // Nothing more to do
    }

    private string PeekNext()
    {
        if (pos < 0)
            // pos < 0 indicates that there are no more tokens
            return null;
        if (pos < tokens.Length)
        {
            if (tokens[pos].Length == 0)
            {
                ++pos;
                return PeekNext();
            }
            return tokens[pos];
        }
        string line = reader.ReadLine();
        if (line == null)
        {
            // There is no more data to read
            pos = -1;
            return null;
        }
        // Split the line that was read on white space characters
        tokens = line.Split(null);
        pos = 0;
        return PeekNext();
    }

    public bool HasNext()
    {
        return (PeekNext() != null);
    }

    public string Next()
    {
        string next = PeekNext();
        if (next == null)
            throw new NoMoreTokensException();
        ++pos;
        return next;
    }
}

public class Scanner : Tokenizer
{

    public int NextInt()
    {
        return int.Parse(Next());
    }

    public long NextLong()
    {
        return long.Parse(Next());
    }

    public float NextFloat()
    {
        return float.Parse(Next());
    }

    public double NextDouble()
    {
        return double.Parse(Next());
    }
}

public class BufferedStdoutWriter : StreamWriter
{
    public BufferedStdoutWriter() : base(new BufferedStream(Console.OpenStandardOutput()))
    {
    }
}
/******************************************************************************/

/*******************************************************************************
* DisjointSet datastructure                                                   */
public struct DisjointSet {
    public int[] parent;
    public int[] rank;
    public DisjointSet(int n) {
        parent = new int[n];
        for (int i = 0; i < n; ++i) {
            parent[i] = i;
        }
        rank = new int[n];
    }

    public int Find(int i) {
        int idx = i;
        var compress = new List<int>();
        while (idx != parent[idx]) {
            compress.Add(idx);
            idx = parent[idx];
        }

        foreach (var e in compress) {   // path compress 
            parent[e] = idx;
        }
        return idx;
    }

    public void Union(int a, int b) {
        int aPar = this.Find(a);
        int bPar = this.Find(b);

        if (rank[aPar] > rank[bPar]) {  // by rank
            parent[bPar] = aPar;
        } else {
            parent[aPar] = bPar;
        }
        if (rank[aPar] == rank[bPar]) {
            ++rank[bPar];
        }
    }
}

class MaxHeap {
    List<int> data;

    public MaxHeap() {
        data = new List<int>();
    }

    public void Add(int a) {
        data.Add(a);
        int idx = data.Count - 1;
        int parent = (int) Math.Floor((double) (idx - 1) / 2);
        while (idx != 0 && (data[idx] > data[parent])) {
            int tmp = data[parent];
            data[parent] = data[idx];
            data[idx] = tmp;

            idx = parent;
            parent = (int) Math.Floor((double) (idx - 1) / 2);
        }
    }

    public int Pop() {
        int res = data[0];
        data[0] = data[data.Count - 1];
        data.RemoveAt(data.Count - 1);

        int idx = 0;
        while (true) {
            int child1 = (2 * idx) + 1;
            int child2 = (2 * idx) + 2;

            if (child1 >= data.Count) { // no children
                break;
            } else if (child2 >= data.Count) {  // one child
                if (data[idx] < data[child1]) {
                    int tmp = data[idx];
                    data[idx] = data[child1];
                    data[child1] = tmp;
                }
                break;
            } else {    // two children
                int maxChild = data[child1] > data[child2] ? child1 : child2;
                if (data[idx] < data[maxChild]) {
                    int tmp = data[idx];
                    data[idx] = data[maxChild];
                    data[maxChild] = tmp;
                    idx = maxChild;
                    continue;
                } else {    // no swap
                    break;
                }
            }
        } 

        return res;           
    }


}


class Dequeue {
    public Dictionary<int, int> data = new Dictionary<int, int>();
    int firstIdx;
    public int Count;
    public Dequeue() {
        data = new Dictionary<int, int>();
        firstIdx = 1;
        Count = 0;
    }

    public void PushFront(int a) {
        data[firstIdx - 1] = a;
        ++Count;
        --firstIdx;
    }

    public void PushBack(int a) {
        data[firstIdx + Count] = a;
        ++Count;
    }

    public int PopFront() {
        --Count;
        ++firstIdx;
        return data[firstIdx - 1];
    }

    public int PopBack() {
        --Count;
        return data[firstIdx + Count];
    }

    public int Get(int n) {
        return data[firstIdx + n];
    }
}
/******************************************************************************/

class MainClass {

    // Debug functions   
    static void debug<T>(IEnumerable<T> a, string s = "") {
        Console.WriteLine($"name: {s}");
        int i = 0;
        foreach (var e in a) {
            Console.WriteLine($"value {i}: {e}");
            ++i;
        }
    }
    static void dbg<T>(T a, string s = "") {
        Console.WriteLine($"name: {s} value: {a}");
    }
    ////////////////////
    
    static int gcd(int a, int b) {
        while (b != 0) {
            int t = b;
            b = a % b;
            a = t;
        }
        return a;
    }


    public static void Main() {
        
        var sc = new Scanner();
        var wr = new BufferedStdoutWriter();
        var dot = new NumberFormatInfo();
        dot.NumberDecimalSeparator = ".";


        long x = sc.NextLong();

        int ans = 0;
        long start = 100;
        while (true) {
            ++ans;
            start = (long)((double) start * 1.01);
            if (start >= x) {
                wr.Write(ans);
                wr.Flush();
                return;
            }
        }
        
    }
}