human
Bear Limak wants to become the largest of bears, or at least to become larger than his brother Bob.

Right now, Limak and Bob weigh a and b respectively. It's guaranteed that Limak's weight is smaller than or equal to his brother's weight.

Limak eats a lot and his weight is tripled after every year, while Bob's weight is doubled after every year.

After how many full years will Limak become strictly larger (strictly heavier) than Bob?

Input

The only line of the input contains two integers a and b (1 ≤ a ≤ b ≤ 10) — the weight of Limak and the weight of Bob respectively.

Output

Print one integer, denoting the integer number of years after which Limak will become strictly larger than Bob.

Examples

Input

4 7

Output

2

Input

4 9

Output

3

Input

1 1

Output

1

Note

In the first sample, Limak weighs 4 and Bob weighs 7 initially. After one year their weights are 4·3 = 12 and 7·2 = 14 respectively (one weight is tripled while the other one is doubled). Limak isn't larger than Bob yet. After the second year weights are 36 and 28, so the first weight is greater than the second one. Limak became larger than Bob after two years so you should print 2.

In the second sample, Limak's and Bob's weights in next years are: 12 and 18, then 36 and 36, and finally 108 and 72 (after three years). The answer is 3. Remember that Limak wants to be larger than Bob and he won't be satisfied with equal weights.

In the third sample, Limak becomes larger than Bob after the first year. Their weights will be 3 and 2 then.
Solve the task in PYTHON3.
 Can you provide a Python code to print one integer, denoting the integer number of years after which Limak will become strictly larger than Bob?
assistant
#Here is Python code to print one integer, denoting the integer number of years after which Limak will become strictly larger than Bob.

#!/usr/bin/env python3
# 791A_brother.py - Codeforces.com/problemset/problem/791/A by Sergey 2017

import unittest
import sys

###############################################################################
# Brother Class (Main Program)
###############################################################################

class Brother:
    """ Brother representation """

    def __init__(self, test_inputs=None):
        """ Default constructor """

        it = iter(test_inputs.split("\n")) if test_inputs else None

        def uinput():
            return next(it) if it else sys.stdin.readline().rstrip()

        # Reading single elements
        [self.a, self.b] = map(int, uinput().split())

    def calculate(self):
        """ Main calcualtion function of the class """

        n = 0
        a = self.a
        b = self.b
        while (a <= b):
            a *= 3
            b *= 2
            n += 1

        result = n

        return str(result)

###############################################################################
# Unit Tests
###############################################################################

class unitTests(unittest.TestCase):

    def test_single_test(self):
        """ Brother class testing """

        # Constructor test
        test = "4 7"
        d = Brother(test)
        self.assertEqual(d.a, 4)
        self.assertEqual(d.b, 7)

        # Sample test
        self.assertEqual(Brother(test).calculate(), "2")

        # Sample test
        test = "4 9\n"
        self.assertEqual(Brother(test).calculate(), "3")

        # Sample test
        test = "1 1\n"
        self.assertEqual(Brother(test).calculate(), "1")

        # My tests
        test = ""
        # self.assertEqual(Brother(test).calculate(), "0")

        # Time limit test
        # self.time_limit_test(5000)

    def time_limit_test(self, nmax):
        """ Timelimit testing """
        import random
        import timeit

        # Random inputs
        test = str(nmax) + " " + str(nmax) + "\n"
        numnums =...