Searching for Nessy 

The Loch Ness Monsteris a mysterious and unidentified animal said to inhabit Loch Ness, 
a large deep freshwater loch near the city of Inverness in northern Scotland. Nessie is usually categorized as a type of lake monster.
http://en.wikipedia.org/wiki/Loch_Ness_Monster

In July 2003, the BBC reported an extensive investigation of Loch Ness by a BBC team, using 600 separate sonar beams, found no trace of any ¨sea monster¨ (i.e., any large animal, known or unknown) in the loch. The BBC team concluded that Nessie does not exist. Now we want to repeat the experiment.

Given a grid of n rows and m columns representing the loch, 6$\le$n, m$\le$10000, find the minimum number s of sonar beams you must put in the square such that we can control every position in the grid, with the following conditions:

• one sonar occupies one position in the grid; the sonar beam controls its own cell and the contiguous cells;
• the border cells do not need to be controlled, because Nessy cannot hide there (she is too big).

For example,

$\parbox{.5\textwidth}{ \begin{center} \mbox{} \epsfbox{p11044.eps} \end{center}}$$\parbox{.49\textwidth}{ \begin{center} \mbox{} \epsfbox{p11044a.eps} \end{center}}$

where X represents a sonar, and the shaded cells are controlled by their sonar beams; the last figure gives us a solution.

Input 

The first line of the input contains an integer, t, indicating the number of test cases. For each test case, there is a line with two numbers separated by blanks, 6$\le$n, m$\le$10000, that is, the size of the grid (n rows and m columns).

Output 

For each test case, the output should consist of one line showing the minimum number of sonars that verifies the conditions above.

Sample Input 

 
3
6 6
7 7
9 13

Sample Output 

 
4
4
12