New Year and Snowy Grid

Description:

Input:

The first line of the input contains three integers h, w and q (2 ≤ h, w ≤ 1000, 1 ≤ q ≤ 10 000) — the height and the width of the grid, and the number of days, respectively.

Next h lines describe which cells are allowed and which permanently blocked. The i-th line contains a string of length w, describing the i-th row. Every character is either '.' (denoting an allowed cell) or '#' (denoting a permanently blocked cell). It's guaranteed that a day with no cells temporarily blocked by snow would be interesting.

Then, the description of q days is given. The description of the i-th day starts with a line containing a single integer k_i (1 ≤ k_i ≤ 10) — the number of cells that are temporarily blocked by snow on that day. Each of next k_i lines contains two integers r_i, j and c_i, j (1 ≤ r_i, j ≤ h, 1 ≤ c_i, j ≤ w), representing a cell at the intersection of the row r_i, j and the column c_i, j. The given k_i cells are distinct and none of them is permanently blocked. Also, none of them contains Limak's house or school.

Output:

For each of q days print "YES" if that day is interesting, and otherwise print "NO", both without the quotes. After printing an answer, you have to both print the end-of-line character and flush the output. Then you can proceed to the next day. You can get Idleness Limit Exceeded if you don't print anything or if you forget to flush the output.

To flush you can use (just after printing a YES/NO and end-of-line):

• fflush(stdout) in C++;
• System.out.flush() in Java;
• stdout.flush() in Python;
• flush(output) in Pascal;
• See the documentation for other languages.

Sample Input:

3 5 4
.....
.....
.#...
1
1 4
1
1 5
2
2 4
3 1
2
1 5
3 3

Sample Output:

NO
YES
YES
NO

Sample Input:

9 31 5
...............................
...............................
.###.###.#.###...###.###.#.###.
...#.#.#.#.#.......#.#.#.#...#.
.###.#.#.#.###...###.#.#.#...#.
.#...#.#.#.#.#...#...#.#.#...#.
.###.###.#.###...###.###.#...#.
...............................
...............................
5
6 5
2 11
1 14
8 15
2 14
5
2 14
1 14
8 16
6 5
2 11
3
2 2
1 4
8 30
10
3 1
3 11
5 16
7 21
4 16
3 5
7 31
3 9
7 25
3 27
10
3 1
3 9
7 25
3 27
7 21
4 17
3 5
7 31
4 16
3 11

Sample Output:

NO
YES
YES
YES
NO

Note:

In the first sample, there are 4 days. Drawings below show how Limak could go to school and return to his home in the second and the third day (on the left and on the right respectively). A permanently blocked cell is painted red, while cells temporarily blocked by snow are painted orange. Black and green arrows should Limak's way to the school and back to the house respectively.

For the second sample, below you can see how the grid looks like on each day, where '#' denotes a cell that is blocked, either temporarily or permanently.