Codeforces Round 905 (Div. 3) |
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Finished |

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time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 $$$1 \leq i < n$$$.

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.

Example

Input

91122 133 2 147 1 5 3511 2 15 7 1061 8 2 16 8 162624323799 708290323122 1 1 3 3 11 12 22 45 777 777 15001212 11 10 9 8 7 6 5 4 3 2 1

Output

0 1 3 6 10 3 0 2 66

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 $$$[3, 4, 4]$$$.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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