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

namespace Practice
{
    class Program
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();

            Console.Out.Flush();
        }
        private const int MOD = 1000000007;
        private const int MAX = 1000001;
        static long[] fac = new long[MAX];
        static long[] finv = new long[MAX];
        static long[] inv = new long[MAX];

        static void Solve()
        {
            var x = Input.NextLong();
            long a = 100;

            int ans = 0;
            while(a < x)
            {
                long d =(long)( a * 0.01);
                a += d;
                ans++;
            }
            Console.WriteLine(ans);
        }


        #region よく使う便利関数

        private static Dictionary<long, int> Factorize(long n)
        {
            var dic = new Dictionary<long, int>();

            for (long i = 2; i * i <= n; ++i)
            {
                while (n % i == 0)
                {
                    if (!dic.ContainsKey(i))
                    {
                        dic.Add(i, 0);
                    }
                    dic[i]++;
                    n /= i;
                }

            }

            if (n != 1)
            {
                dic.Add(n, 1);
            }
            return dic;
        }
        static void COMinit()
        {
            fac[0] = fac[1] = 1;
            finv[0] = finv[1] = 1;
            inv[1] = 1;
            for (int i = 2; i < MAX; i++)
            {
                fac[i] = fac[i - 1] * i % MOD;
                inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
                finv[i] = finv[i - 1] * inv[i] % MOD;
            }
        }

        // 二項係数計算
        static long COM(long n, long k)
        {
            if (n < k) return 0;
            if (n < 0 || k < 0) return 0;
            return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
        }

        static class Input
        {
            static char[] separator = { ' ' };
            public static bool IsEof { get; set; }
            static Queue<string> q { get; set; }

            static Input()
            {
                IsEof = false;
                q = new Queue<string>();
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            /// <param name="items"></param>
            public static void SetText(IEnumerable<string> items)
            {
                foreach (var item in items)
                {
                    SetText(item);
                }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            /// <param name="s"></param>
            /// <returns></returns>
            public static bool SetText(string s)
            {
                if (s == null) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    q.Enqueue(elem);
                }

                return true;
            }

            /// <summary>
            /// 内部queueに入力からの値をsplitして格納する
            /// </summary>
            /// <returns></returns>
            static bool read()
            {
                var s = Console.ReadLine();
                if (s == null) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    q.Enqueue(elem);
                }

                if (!q.Any()) return read();

                return true;
            }

            /// <summary>
            /// 次のstringを一つ読み込む
            /// </summary>
            /// <returns></returns>
            public static string Next()
            {
                if (!q.Any())
                {
                    if (!read())
                    {
                        IsEof = true;
                        return "";
                    }
                }

                return q.Dequeue();
            }

            public static int NextInt() => int.Parse(Next());
            public static long NextLong() => long.Parse(Next());
            public static double NextDouble() => double.Parse(Next());

            public static List<string> Next(int n) => Enumerable.Range(0, n).Select(_ => Next()).ToList();
            public static List<int> NextInt(int n) => Next(n).Select(x => int.Parse(x)).ToList();
            public static List<long> NextLong(int n) => Next(n).Select(x => long.Parse(x)).ToList();
            public static List<double> NextDouble(int n) => Next(n).Select(x => double.Parse(x)).ToList();

            public static List<string> NextLine() => Console.ReadLine().Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries).ToList();
            public static List<int> NextIntLine() => NextLine().Select(x => int.Parse(x)).ToList();
            public static List<long> NextLongLine() => NextLine().Select(x => long.Parse(x)).ToList();
            public static List<double> NextDoubleLine() => NextLine().Select(x => double.Parse(x)).ToList();
        }
        private static bool isPrime(long x)
        {
            if (x == 2) { return true; }
            if (x < 2 || x % 2 == 0) { return false; }
            long i = 3;
            while (i * i <= x)
            {
                if (x % i == 0) { return false; }
                i = i + 2;
            }
            return true;
        }
        private static long lcm(long x, long y)
        {
            return x / gcd(x, y) * y;
        }
        private static long gcd(long x, long y)
        {
            return y > 0 ? gcd(y, x % y) : x;
        }
        private static long pow(long x, long n)
        {
            if (n == 0) { return 1; }
            long res = pow(x * x % MOD, n / 2);
            if (n % 2 == 1)
            {
                res = res * x % MOD;
            }
            return res;
        }
        private static void Swap<T>(ref T x, ref T y)
        {
            T t = x;
            x = y;
            y = t;
        }

        /// <summary>
        /// 指定した値以上の先頭のインデクスを返す
        /// </summary>
        /// <typeparam name="T">比較する値の型</typeparam>
        /// <param name="arr">対象の配列（※ソート済みであること）</param>
        /// <param name="start">開始インデクス [inclusive]</param>
        /// <param name="end">終了インデクス [exclusive]</param>
        /// <param name="value">検索する値</param>
        /// <param name="comparer">比較関数(インターフェイス)</param>
        /// <returns>指定した値以上の先頭のインデクス</returns>
        public static int LowerBound<T>(IReadOnlyList<T> arr, int start, int end, T value, IComparer<T> comparer)
        {
            int low = start;
            int high = end;
            int mid;
            while (low < high)
            {
                mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) < 0)
                    low = mid + 1;
                else
                    high = mid;
            }
            return low;
        }

        //引数省略のオーバーロード
        public static int LowerBound<T>(IReadOnlyList<T> arr, T value) where T : IComparable
        {
            return LowerBound(arr, 0, arr.Count, value, Comparer<T>.Default);
        }

        /// <summary>
        /// 指定した値より大きい先頭のインデクスを返す
        /// </summary>
        /// <typeparam name="T">比較する値の型</typeparam>
        /// <param name="arr">対象の配列（※ソート済みであること）</param>
        /// <param name="start">開始インデクス [inclusive]</param>
        /// <param name="end">終了インデクス [exclusive]</param>
        /// <param name="value">検索する値</param>
        /// <param name="comparer">比較関数(インターフェイス)</param>
        /// <returns>指定した値より大きい先頭のインデクス</returns>
        public static int UpperBound<T>(IReadOnlyList<T> arr, int start, int end, T value, IComparer<T> comparer)
        {
            int low = start;
            int high = end;
            int mid;
            while (low < high)
            {
                mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) <= 0)
                    low = mid + 1;
                else
                    high = mid;
            }
            return low;
        }

        //引数省略のオーバーロード
        public static int UpperBound<T>(IReadOnlyList<T> arr, T value)
        {
            return UpperBound(arr, 0, arr.Count, value, Comparer<T>.Default);
        }
#endregion
    }

    public class DisjointSet
    {
        private int[] rank;
        private int[] p;
        private int[] size;
        public DisjointSet(int n)
        {
            rank = new int[n];
            p = new int[n];
            size = new int[n];
            for (int i = 0; i < n; ++i)
            {
                MakeSet(i);
            }
        }
        public void MakeSet(int x)
        {
            p[x] = x;
            rank[x] = 0;
            size[x] = 1;
        }
        public bool IsSame(int x, int y)
        {
            return FindSet(x) == FindSet(y);
        }
        public void Unite(int x, int y)
        {
            Link(FindSet(x), FindSet(y));
        }
        public void Link(int x, int y)
        {
            if (rank[x] > rank[y])
            {
                p[y] = x;
                size[x] += size[y];
                size[y] = 0;
            }
            else
            {
                p[x] = y;
                size[y] += size[x];
                size[x] = 0;
                if (rank[x] == rank[y])
                {
                    rank[y]++;
                }
            }
        }
        public int FindSet(int x)
        {
            if (x != p[x])
            {
                p[x] = FindSet(p[x]);
            }
            return p[x];
        }
        public int Size(int x)
        {
            int root = FindSet(x);
            return size[root];
        }
    }
    public class PriorityQueue<T> where T : IComparable
    {
        private IComparer<T> _comparer = null;
        private int _type = 0;

        private T[] _heap;
        private int _sz = 0;

        private int _count = 0;

        /// <summary>
        /// Priority Queue with custom comparer
        /// </summary>
        public PriorityQueue(int maxSize, IComparer<T> comparer)
        {
            _heap = new T[maxSize];
            _comparer = comparer;
        }

        /// <summary>
        /// Priority queue
        /// </summary>
        /// <param name="maxSize">max size</param>
        /// <param name="type">0: asc, 1:desc</param>
        public PriorityQueue(int maxSize, int type = 0)
        {
            _heap = new T[maxSize];
            _type = type;
        }

        private int Compare(T x, T y)
        {
            if (_comparer != null) return _comparer.Compare(x, y);
            return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
        }

        public void Push(T x)
        {
            _count++;

            //node number
            var i = _sz++;

            while (i > 0)
            {
                //parent node number
                var p = (i - 1) / 2;

                if (Compare(_heap[p], x) <= 0) break;

                _heap[i] = _heap[p];
                i = p;
            }

            _heap[i] = x;
        }

        public T Pop()
        {
            _count--;

            T ret = _heap[0];
            T x = _heap[--_sz];

            int i = 0;
            while (i * 2 + 1 < _sz)
            {
                //children
                int a = i * 2 + 1;
                int b = i * 2 + 2;

                if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

                if (Compare(_heap[a], x) >= 0) break;

                _heap[i] = _heap[a];
                i = a;
            }

            _heap[i] = x;

            return ret;
        }

        public int Count()
        {
            return _count;
        }

        public T Peek()
        {
            return _heap[0];
        }

        public bool Contains(T x)
        {
            for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
            return false;
        }

        public void Clear()
        {
            while (this.Count() > 0) this.Pop();
        }

        public IEnumerator<T> GetEnumerator()
        {
            var ret = new List<T>();

            while (this.Count() > 0)
            {
                ret.Add(this.Pop());
            }

            foreach (var r in ret)
            {
                this.Push(r);
                yield return r;
            }
        }

        public T[] ToArray()
        {
            T[] array = new T[_sz];
            int i = 0;

            foreach (var r in this)
            {
                array[i++] = r;
            }

            return array;
        }
    }
}