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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

//type
#define ll long long
typedef pair<int, int> P;
//定数
#define INF 1000000000000 //10^12:∞
#define MOD 1000000007    //10^9+7:合同式の法
#define MAXR 100000       //10^5:配列の最大のrange
//略記
#define PB push_back //挿入
#define MP make_pair //pairのコンストラクタ
#define F first      //pairの一つ目の要素
#define S second     //pairの二つ目の要素
#define Z class

// input
#define INIT                          \
    std::ios::sync_with_stdio(false); \
    std::cin.tie(0);
#define VAR(type, ...) \
    type __VA_ARGS__;  \
    MACRO_VAR_Scan(__VA_ARGS__);
template <typename T>
void MACRO_VAR_Scan(T &t)
{
    std::cin >> t;
}
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First &first, Rest &... rest)
{
    std::cin >> first;
    MACRO_VAR_Scan(rest...);
}
#define VEC_ROW(type, n, ...)                \
    std::vector<type> __VA_ARGS__;           \
    MACRO_VEC_ROW_Init(n, __VA_ARGS__);      \
    for (int w_ = 0; w_ < n; ++w_)           \
    {                                        \
        MACRO_VEC_ROW_Scan(w_, __VA_ARGS__); \
    }
template <typename T>
void MACRO_VEC_ROW_Init(int n, T &t)
{
    t.resize(n);
}
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First &first, Rest &... rest)
{
    first.resize(n);
    MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T>
void MACRO_VEC_ROW_Scan(int p, T &t) { std::cin >> t[p]; }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First &first, Rest &... rest)
{
    std::cin >> first[p];
    MACRO_VEC_ROW_Scan(p, rest...);
}
#define VEC(type, c, n)     \
    std::vector<type> c(n); \
    for (auto &i : c)       \
        std::cin >> i;
// 2d vector:  MAT(type, v, size, size);
#define MAT(type, c, m, n)                                     \
    std::vector<std::vector<type>> c(m, std::vector<type>(n)); \
    for (auto &R : c)                                          \
        for (auto &w : R)                                      \
            std::cin >> w;

// output
template <typename T>
void MACRO_OUT(const T t) { std::cout << t; }

#define OUT(...) MACRO_OUT(__VA_ARGS__);
#define SP std::cout << " ";
#define TAB std::cout << "\t";
#define BR std::cout << "\n";
#define ENDL std::cout << std::endl;

#define YES() printf("YES\n")
#define NO() printf("NO\n")
#define isYES(x) printf("%s\n", (x) ? "YES" : "NO")
#define Yes() printf("Yes\n")
#define No() printf("No\n")
#define yes() printf("yes\n")
#define no() printf("no\n")
#define ln cout << '\n'
template <Z A>
void pr(A a)
{
    cout << a;
    ln;
}
template <Z A, Z B>
void pr(A a, B b)
{
    cout << a << ' ' << b << endl;
}

// OTHER
// xの二乗を返す (関数テンプレート版)
template <typename T>
T square(T x) { return x * x; }
template <class T>
T GCD(T a, T b)
{
    T r;
    while (a)
        r = b, b = a, a = r % a;
    return b;
}
template <class T>
T LCM(T a, T b) { return a / GCD(a, b) * b; }

#define chmax(x, y) (x = max(x, y))
#define chmin(x, y) (x = min(x, y))
// loop
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define repe(i, n) for (ll i = 0; i <= (n); i++)
#define repd(i, n) for (ll i = n; i > 0; i--)
#define repde(i, n) for (ll i = n; i >= 0; i--)
#define FOR(i, a, b) for (ll i = a; i < (b); i++)
#define FORE(i, a, b) for (ll i = a; i <= (b); i++)
#define FORD(i, a, b) for (ll i = a; i >= (b); i--)
#define FORA(i, I) for (const auto &i : I)

// vector
#define ALL(x) x.begin(), x.end()
typedef vector<int> vi;
typedef vector<string> vs;
typedef vector<vi> vvi;
typedef vector<ll> vl;
#define ERASE(x) x.erase(unique(ALL(x)), x.end()); // erase same elements

bool yes = 0;
bool boo = 0;
int maxx = -100000, minn = 100000;
int sum = 0;

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
// cout << (conditon ? (result:  == 1 ): (==0)) << endl; <- output result of if
// long long 型が表せる値の上限はおよそ 9 × 10＾18 です．

// vector
// sum: accumulate(ALl(x),0)
signed main()
{

    VAR(long long, x);
    long long ans = 100;
    long long a = 0;
    while (ans < x)
    {
        ans *= 1.01;
        if (ans >= x)
        {
            pr(a);
            return 0;
        }
        a++;
    }

    return 0;
}