You have a suitcase with length $X$, width $Y$ and height $Z$. You also have a very comfortable blanket. It has length $L$, width $W$and thickness $H$. You love your blanket very much. You like to take it with you, wherever you go. To fit the blanket in your suitcase, you can apply a fold operation on the blanket.

One fold operation is as follows:

Divide the length or width by $2$.

Multiply the thickness by $2$.

The blanket fits if you can keep it in the suitcase in an axis aligned way. Formally, at least one corner of the blanket must exactly coincide with a corner of the suitcase keeping the entire blanket inside.

Your task is to find the minimum number of fold operations required to fit the blanket in the suitcase. Or report if it is impossible.

Note that it is not necessary to keep the suitcase in input orientation of$X$*$Y$*$Z$, as long as the orientation is axis aligned.

Input

The first line contains an integer $T( 1 \leq T \leq 10^5)$ the number of test cases. Each of the next $T$ lines describe a test case with $6$ space separated integers $X, Y, Z, L, W, H$. Each of these $6$ integers are greater than $0$ and do not exceed $10^9$.

Output

For each test case print a single integer in a separate line. Print the minimum number of fold required to fit the blanket. If impossible, print $-1$.

In the first case, you can fold the length $4$ times to obtain $(L, W, H) = (100, 100, 96)$. In the second case, no sequence of operation can make it possible. In the third case, after fold-ing the length and width $1$ time and $4$ times respectively, you can obtain $(L, W, H) = (2048, 1024, 32)$. Which fits the suitcase exactly. A suitcase$(32, 1024, 2048)$can be oriented in an axis aligned way to$(2048, 1024, 32)$. In the fourth case, it already fits. So no operation is necessary.