You are given a set $$$S$$$, which contains the first $$$n$$$ positive integers: $$$1, 2, \ldots, n$$$.

You can perform the following operation on $$$S$$$ any number of times (possibly zero):

Choose a positive integer $$$k$$$ where $$$1 \le k \le n$$$, such that there exists a multiple of $$$k$$$ in $$$S$$$. Then, delete the smallest multiple of $$$k$$$ from $$$S$$$. This operation requires a cost of $$$k$$$.

You are given a set $$$T$$$, which is a subset of $$$S$$$. Find the minimum possible total cost of operations such that $$$S$$$ would be transformed into $$$T$$$. We can show that such a transformation is always possible.

Input

The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 10\,000$$$) — the number of test cases. The description of the test cases follows.

The first line contains a single positive integer $$$n$$$ ($$$1 \le n \le 10^6$$$).

The second line of each test case contains a binary string of length $$$n$$$, describing the set $$$T$$$. The $$$i$$$-th character of the string is '1' if and only if $$$i$$$ is an element of $$$T$$$, and '0' otherwise.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^6$$$.

Output

For each test case, output one non-negative integer — the minimum possible total cost of operations such that $$$S$$$ would be transformed into $$$T$$$.

Note

In the first test case, we shall not perform any operations as $$$S$$$ is already equal to $$$T$$$, which is the set $$$\{1, 2, 3, 4, 5, 6\}$$$.

In the second test case, initially, $$$S = \{1, 2, 3, 4, 5, 6, 7\}$$$, and $$$T = \{1, 2, 4, 7\}$$$. We shall perform the following operations:

Choose $$$k=3$$$, then delete $$$3$$$ from $$$S$$$.
Choose $$$k=3$$$, then delete $$$6$$$ from $$$S$$$.
Choose $$$k=5$$$, then delete $$$5$$$ from $$$S$$$.

The total cost is $$$3+3+5 = 11$$$. It can be shown that this is the smallest cost possible.

In the third test case, initially, $$$S = \{1, 2, 3, 4\}$$$ and $$$T = \{\}$$$ (empty set). We shall perform $$$4$$$ operations of $$$k=1$$$ to delete $$$1$$$, $$$2$$$, $$$3$$$, and $$$4$$$.

In the fourth test case, initially, $$$S = \{1, 2, 3, 4\}$$$ and $$$T = \{3\}$$$. We shall perform two operations with $$$k=1$$$ to delete $$$1$$$ and $$$2$$$, then perform one operation with $$$k=2$$$ to delete $$$4$$$.

Removing Smallest Multiples

Examples