You are given an array of integers $a_1, a_2, \ldots, a_n$. You need to make it non-decreasing with the minimum number of operations. In one operation, you do the following:

• Choose an index $1 \leq i \leq n$,
• Set $a_i = a_i \cdot 2$.

An array $b_1, b_2, \ldots, b_n$ is non-decreasing if $b_i \leq b_{i+1}$ for all $1 \leq i \lt n$.

Input

Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases. This is followed by their description.

The first line of each test case contains an integer $n$ ($1 \leq n \leq 10^5$) — the size of the array $a$.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 10^9$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

Output

For each test case, output the minimum number of operations needed to make the array non-decreasing.

Note

No operations are needed in the first test case.

In the second test case, we need to choose $i = 2$, after which the array will be $[2, 2]$.

In the third test case, we can apply the following operations:

• Choose $i = 3$, after which the array will be $[3, 2, 2]$,
• Choose $i = 3$, after which the array will be $[3, 2, 4]$,
• Choose $i = 2$, after which the array will be $[3, 4, 4]$.