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.

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熊利馬克想成為最大的熊，或者至少比他的兄弟鮑勃更大。

現(xiàn)在，Limak 和 Bob 分別稱重 a 和 b。 保證利馬克的體重小于或等于他哥哥的體重。

利馬克吃得很多，他的體重每年都會(huì)增加兩倍，而鮑勃的體重每年都會(huì)增加一倍。

多少年后，利馬克會(huì)變得比鮑勃嚴(yán)格更大（嚴(yán)格重）？

輸入

輸入中唯一的一行包含兩個(gè)整數(shù) a 和 b (1?≤?a?≤?b?≤?10)——分別是 Limak 的權(quán)重和 Bob 的權(quán)重。