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.Numerics;
using System.Collections;
using System.Collections.Generic;
using System.Runtime.CompilerServices;
using System.IO;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;
using static Ex;
using System.Runtime.InteropServices.ComTypes;
using System.Net.Mail;
using Microsoft.VisualBasic;
using System.Reflection.PortableExecutable;
using System.Net.Http.Headers;


class AC
{
    /*------------------------------------------------------------------*/

    void Solve()
    {
        io.I(out BigInteger X);
        var c = new BigInteger(100);
        var y = 0;
        while(c < X)
        {
            c *= 101;
            c /= 100;
            y++;
        }
        y.Prt();
    }
    /*------------------------------------------------------------------*/
    void Test()
    {
        //--- TEST ---//
    }
    public static void Main(string[] args) => new AC().Stream();
    IO io = new IO();
    private void Stream()
    {
        /*
        var exStdIn = new System.IO.StreamReader("stdin.txt");
        SetIn(exStdIn);
        Test();
        */
        Solve();
        io.Flush();
    }
}
class IO
{
    #region INPUT
    #region FastRead
    private const int Size = 1 << 12;
    private readonly Stream _stream = OpenStandardInput();
    private readonly byte[] _buffer = new byte[Size];
    private int _ptr = 0, _buffLen = 0;
    private bool HasNextByte()
    {
        if (_ptr < _buffLen) return true;
        _ptr = 0;
        _buffLen = _stream.Read(_buffer, 0, Size);
        return _buffLen > 0;
    }
    private byte ReadByte() => HasNextByte() ? _buffer[_ptr++] : throw new EndOfStreamException();

    private bool IsAscii(int c) => '!' <= c && c <= '~';
    private char NextChar()
    {
        var b = ReadByte();
        while (!IsAscii(b)) b = ReadByte();
        return (char)b;
    }
    private string Next()
    {
        var sb = new StringBuilder();
        for (var b = NextChar(); IsAscii(b); b = (char)ReadByte()) sb.Append(b);
        return sb.ToString();
    }
    public string String => Next();
    public char Char => NextChar();
    public int Int => int.Parse(Next());
    public long Long => long.Parse(Next());
    public double Double => double.Parse(Next());
    #endregion
    #region LazyRead
    private void Scan<T>(ref T x)
    {
        if (x is int) __refvalue(__makeref(x), int) = int.Parse(Next());
        else if (x is long) __refvalue(__makeref(x), long) = long.Parse(Next());
        else if (x is double) __refvalue(__makeref(x), double) = double.Parse(Next());
        else if (x is char) __refvalue(__makeref(x), char) = NextChar();
        else if (x is uint) __refvalue(__makeref(x), uint) = uint.Parse(Next());
        else if (x is ulong) __refvalue(__makeref(x), ulong) = ulong.Parse(Next());
        else if (x is decimal) __refvalue(__makeref(x), decimal) = decimal.Parse(Next());
        else if (x is BigInteger) __refvalue(__makeref(x), BigInteger) = BigInteger.Parse(Next());
        else __refvalue(__makeref(x), string) = Next();
    }
    public void I<T>(out T t)
    {
        t = default;
        Scan(ref t);
    }

    public void I<T, TU>(out T t, out TU u)
    {
        I(out t);
        I(out u);
    }
    public void I<T, TU, TV>(out T t, out TU u, out TV v)
    {
        I(out t, out u);
        I(out v);
    }
    public void I<T, TU, TV, TW>(out T t, out TU u, out TV v, out TW w)
    {
        I(out t, out u);
        I(out v, out w);
    }
    public void I<T, TU, TV, TW, TX>(out T t, out TU u, out TV v, out TW w, out TX x)
    {
        I(out t, out u, out v);
        I(out w, out x);
    }
    public void I<T, TU, TV, TW, TX, TY>(out T t, out TU u, out TV v, out TW w, out TX x, out TY y)
    {
        I(out t, out u, out v);
        I(out w, out x, out y);
    }
    public void I<T>(out T[] a, int n)
    {
        T[] ts = new T[n];
        a = ts;
        for (int i = 0; i < n; ++i) I(out a[i]);
    }
    public void I<T, TU>(out T[] a, out TU[] b, int n)
    {
        a = new T[n];
        b = new TU[n];
        for (int i = 0; i < n; ++i) I(out a[i], out b[i]);
    }
    public void I<T, TU, TV>(out T[] a, out TU[] b, out TV[] c, int n)
    {
        a = new T[n];
        b = new TU[n];
        c = new TV[n];
        for (var i = 0; i < n; ++i) I(out a[i], out b[i], out c[i]);
    }
    public void I<T>(out T[,] a, int h, int w)
    {
        a = new T[h, w];
        for (int i = 0; i < h; ++i) for (int j = 0; j < w; ++j) I(out a[i, j]);
    }
    #endregion
    #endregion
    #region OUTPUT
    private readonly StreamWriter _sw = new StreamWriter(OpenStandardOutput())
    {
#if DEBUG
        AutoFlush = true
#else
        AutoFlush = false
#endif
    };
    public void Flush() => Out.Flush();
    public void YN(bool f) => yn(f, "YES", "NO");
    public void Yn(bool f) => yn(f, "Yes", "No");
    public void yn(bool f, string y = "yes", string n = "no") => WriteLine(f ? y : n);
    #endregion
    public IO() { SetOut(_sw); }
}
static class Ex
{
    #region マクロもどき
    public static T ID<T>(T x) => x;
    public static Dictionary<T1, T2> MERGE<T1, T2>(Dictionary<T1, T2> xs, Dictionary<T1, T2> ys) => xs.Except(xs.Join(ys, z => z.Key, z => z.Key, (a, b) => a)).Concat(ys).ToDictionary(z => z.Key, z => z.Value);
    public static void FOR(int a, int b, Action<int> f) => FOR(a, b, 1, f);
    public static void FOR(int a, int b, int n, Action<int> f)
    {
        for (int i = a; i < b; i += n) f(i);
    }
    public static void REP(int a, Action<int> f) => FOR(0, a, f);
    public static void REPEQ(int a, Action<int> f) => FOR(0, a + 1, f);
    public static void FOREQ(int a, int b, Action<int> f) => FOR(a, b + 1, f);
    public static void FOREQ(int a, int b, int n, Action<int> f) => FOR(a, b + 1, n, f);
    public static void REP(int a, int b, Action<int, int> f) => REP(a, i => REP(b, j => f(i, j)));
    public static void REP(int a, int b, int c, Action<int, int, int> f) => REP(a, i => REP(b, j => REP(c, k => f(i, j, k))));
    public static void REPEQ(int a, int b, Action<int, int> f) => REPEQ(a, i => REPEQ(b, j => f(i, j)));
    public static void REPEQ(int a, int b, int c, Action<int, int, int> f) => REPEQ(a, i => REPEQ(b, j => REPEQ(c, k => f(i, j, k))));
    public static T MIN<T>(params T[] xs) => xs.Min();
    public static T MAX<T>(params T[] xs) => xs.Max();
    public static IEnumerable<int> RANGE(int s, int e) => Enumerable.Range(s, e - s + 1);
    public static int LCM(int a, int b) => a * (b / GCD(a, b));
    public static int GCD(int a, int b) => (a < b) ? GCD(b, a) : b == 0 ? a : GCD(b, a % b);
    public static int LCM(params int[] xs) => xs.Aggregate(LCM);
    public static int GCD(params int[] xs) => xs.Aggregate(GCD);
    public static long LCM(long a, long b) => a * (b / GCD(a, b));
    public static long GCD(long a, long b) => (a < b) ? GCD(b, a) : b == 0L ? a : GCD(b, a % b);
    public static long LCM(params long[] xs) => xs.Aggregate(LCM);
    public static long GCD(params long[] xs) => xs.Aggregate(GCD);
    #endregion
    #region 拡張メソッド
    public static void Rep(this int x, Action<int> f) => REP(x, f);
    public static void RepEq(this int x, Action<int> f) => REPEQ(x, f);
    public static int ToInt(this string s)
    {
        int.TryParse(s.TrimStart('0'), out int n);
        return n;
    }
    public static int ToInt(this char c) => ToInt(c.ToString());
    public static int ToInt(this char[] c) => ToInt(new string(c));
    public static long ToLong(this string s)
    {
        long.TryParse(s.TrimStart('0'), out long n);
        return n;
    }
    public static long ToLong(this int x) => (long)x;
    public static IEnumerable<long> ToLong(this IEnumerable<int> xs) => xs.Select(x => x.ToLong());
    public static long ToLong(this char c) => ToLong(c.ToString());
    public static long ToLong(this char[] c) => ToLong(new string(c));
    public static int ToMod(this int x, int mod = (int)(1e9 + 7)) => x % mod;
    public static long ToMod(this long x, long mod = (long)(1e9 + 7)) => x % mod;
    public static void Do<T>(this T x, Action<T> f) => f(x);
    public static TU Then<T, TU>(this T x, Func<T, TU> f) => f(x);
    public static bool IsIn<T>(this T[] xs, int i) => 0 <= i && i < xs.Length;
    public static bool IsIn<T>(this T[,] xxs, int i, int j) => 0 <= i && i < xxs.GetLength(0) && 0 <= j && j < xxs.GetLength(1);
    public static void Iter<T>(this IEnumerable<T> xs, Action<T> f)
    {
        foreach (var x in xs) f(x);
    }
    public struct IndexedItem<T>
    {
        public int Index;
        public T Value;
        public IndexedItem(int idx, T val) => (Index, Value) = (idx, val);
    }
    public static IEnumerable<IndexedItem<T>> Indexed<T>(this IEnumerable<T> xs) => xs.Select((x, i) => new IndexedItem<T>(i, x));
    public static void Set<T>(this T[] xs, T v) => REP(xs.Length, i => xs[i] = v);
    public static void Set<T>(this T[,] xxs, T v) => REP(xxs.GetLength(0), i => REP(xxs.GetLength(1), j => xxs[i, j] = v));
    public static string Pad0<T>(this T s, int n) => s.ToString().PadLeft(n, '0');
    public static int RoundOff(this double v, int n) => (int)Round(v, n - 1, MidpointRounding.AwayFromZero);
    public static int RoundUp(this double v) => (int)Ceiling(v);
    public static int RoundDown(this double v) => (int)Floor(v);
    public static bool Odd(this int v) => (v & 1) != 0;
    public static bool Odd(this long v) => (v & 1) != 0;
    public static bool Eve(this int v) => !v.Odd();
    public static bool Eve(this long v) => !v.Odd();
    public static void Prt<T>(this T x) => WriteLine(x);
    public static void Prt<T>(this T[] xs) => xs.Iter(x => WriteLine(x));
    public static void Prt<T>(this List<T> xs) => xs.Iter(x => WriteLine(x));
    public static void Prt<T>(this T[,] xs) => xs.GetLength(0).Rep(i =>
    {
        xs.GetLength(1).Rep(j => Write($"{xs[i, j]} "));
        WriteLine();
    });
    public static void Prt_<T>(this T[] xs) => WriteLine(string.Join(" ", xs));
    public static void Log<T>(this T x, [CallerLineNumber] int line = 0)
    {
#if DEBUG
        Error.WriteLine($"--- LOG[{line}]: {x} ---");
#endif
    }
    public static void Log<T>(this T[] xs, [CallerLineNumber] int line = 0)
    {
#if DEBUG
        Error.WriteLine($"^^^ LOG[{line}] ^^^");
        xs.Iter(x => Error.WriteLine(x));
        Error.WriteLine($"vvv LOG[{line}] vvv\n");
#endif
    }
    public static void Log<T>(this T[,] xs, [CallerLineNumber] int line = 0)
    {
#if DEBUG
        Error.WriteLine($"^^^ LOG[{line}] ^^^");
        xs.GetLength(0).Rep(i =>
        {
            xs.GetLength(1).Rep(j => Error.Write($"{xs[i, j]} "));
            Error.WriteLine();
        });
        Error.WriteLine($"vvv LOG[{line}] vvv\n");
#endif
    }
    public static string Reversed(this string s) => string.Join("", s.Reverse());
    public static string Repeat(this string s, int n) => string.Concat(Enumerable.Repeat(s, n));
    #endregion
}