Problem

time limit per test : 2 seconds
memory limit per test : 256 megabytes
input : standard input
output : standard output

Description

You are given a picture consisting of $nn$ rows and $m$ columns. Rows are numbered from $1$ to $n$ from the top to the bottom, columns are numbered from $1$ to $m$ from the left to the right. Each cell is painted either black or white.

You think that this picture is not interesting enough. You consider a picture to be interesting if there is at least one cross in it. A cross is represented by a pair of numbers $x$ and $y$ , where $1≤x≤n$ and $1≤y≤m$, such that all cells in row $x$ and all cells in column $y$ are painted black.

For examples, each of these pictures contain crosses:

The fourth picture contains 4 crosses: at $(1,3)$ , (1,5)(1,5), $(3,3)$ and $(3,5)$ .

Following images don’t contain crosses:

You have a brush and a can of black paint, so you can make this picture interesting. Each minute you may choose a white cell and paint it black.

What is the minimum number of minutes you have to spend so the resulting picture contains at least one cross?

Input

The first line contains an integer $q$ (1≤q≤5⋅1041≤q≤5⋅104) — the number of queries.

The first line of each query contains two integers $nn$ and $m$ (1≤n,m≤5⋅1041≤n,m≤5⋅104, n⋅m≤4⋅105n⋅m≤4⋅105) — the number of rows and the number of columns in the picture.

Each of the next $nn$ lines contains $m$ characters — ‘.’ if the cell is painted white and ‘*’ if the cell is painted black.

It is guaranteed that $\sum n\le5\times10^4, \sum n\times m \le 4 \times 10^5$.

Output

Print $q$ lines, the $i$-th line should contain a single integer — the answer to the $i$-th query, which is the minimum number of minutes you have to spend so the resulting picture contains at least one cross.

Example

output

Note

The example contains all the pictures from above in the same order.

The first 5 pictures already contain a cross, thus you don’t have to paint anything.

You can paint $(1,3)$ , $(3,1)$ , $(5,3)$ and $(3,5)$ on the 66-th picture to get a cross in $(3,3)$ . That’ll take you 44 minutes.

You can paint $(1,2)$ on the $7$-th picture to get a cross in $(4,2)$ .

You can paint $(2,2)$ on the 88-th picture to get a cross in $(2,2)$. You can, for example, paint $(1,3)$ , $(3,1)$ and $(3,3)$ to get a cross in $(3,3)$ but that will take you 33 minutes instead of $1$ .

There are 9 possible crosses you can get in minimum time on the 99-th picture. One of them is in $(1,1)$ : paint $(1,2)$ and $(2,1)$ .

❤采之欲遗谁，所思在远道。❤
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