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: Accepted)

// 未解決

#include <bits/stdc++.h>

#include <iostream>
using namespace std;

#define EACH(i, a) for (auto &&i : a)
#define FOR(i, a, b) for (int i = (int)a; i < (int)b; ++i)
#define RFOR(i, a, b) for (int i = (int)b - 1; i >= (int)a; --i)
#define REP(i, n) FOR(i, 0, n)
#define REPS(i, n) FOR(i, 1, int(n) + 1)
#define RREP(i, n) RFOR(i, 0, n)
#define RREPS(i, n) RFOR(i, 1, int(n) + 1)
#define ALL(x) (x).begin(), (x).end()
#define MEMSET(v, h) memset((v), h, sizeof(v))
#define debug(x) cout << #x << ": " << x << endl

#define pb push_back
#define mp make_pair
#define F first
#define S second

#define y0 y3487465
#define y1 y8687969
#define j0 j1347829
#define j1 j234892
#define next asdnext
#define prev asdprev
#define INF (1L << 30)
#define MOD (1000000007)
int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

template <class T>
void pv(T a, T b) {
  for (T i = a; i != b; ++i) cout << *i << " ";
  cout << endl;
}
template <class T>
void pvp(T a, T b) {
  for (T i = a; i != b; ++i)
    cout << "(" << i->first << ", " << i->second << ") ";
  cout << endl;
}
template <class T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
int in() {
  int x;
  scanf("%d", &x);
  return x;
}

using ll = long long;
#define int ll

//**********

signed main(void) {
  ios::sync_with_stdio(false);
  cin.tie(0);

  int x;
  cin >> x;
  int a = 100;
  int ans = 0;
  while (a < x && ans < 3500) {
    a = a * 101 / 100;
    // debug(a);
    ans += 1;
  }
  a /= 10000.00;
  x /= 10000.00;
  while (a < x) {
    a = a * 101 / 100;
    // debug(a);
    ans += 1;
  }
  cout << ans << endl;

  return 0;
};