Read problems statements in Mandarin Chinese, Russian and Vietnamese as well.

Xenny reverse-engineered all the binaries released by the International Security Agency (ISA)
during summer vacation just to pass time. As a reward, the ISA gave him infinite ByteCoins.

Out of sheer boredom and a sense of purposelessness in life, Xenny decided to arrange the Coins on a 2-Dimensional Euclidean Plane.
The boredom was so strong that he arranged these coins in a specific pattern, as opposed to the usual, monotonous way of storing coins in a Piggy Bank.

On each integer co-ordinate (x, y) where x ≥ 0 and y ≥ 0, a single coin was placed. And each coin was assigned a rank. The following pattern was followed in the arrangement:

Let's denote the co-ordinates of the k^{th} coin by (x_{k}, y_{k}) and its rank by R_{k}.

For any 2 coins i, j:

if (x_{i} + y_{i}) < (x_{j} + y_{j}) or ( (x_{i} + y_{i}) == (x_{j} + y_{j}) and x_{i} < x_{j})

then R_{i} < R_{j}. We sort all the coins by this comparison.

The index of the coin (C) in this sorted list of coins (1-indexed) is its rank.

Each query is as follows: Given (U, V). Among the coins that are lying on or inside the rectangle with
its diagonal end-points being (0, 0) and (U, V),
which is the coin that has the maximum rank?

------ Input ------

The first line contains an integer, T - the number of testcases.

Each testcase contains 2 space-separated integers: U, V.

------ Output ------

For each testcase, print the rank of the maximum ranked coin, on a new line.

------ Constraints ------

Subtask 1: (40 points)
$1 ≤ T ≤ 100$
$1 ≤ U, V ≤ 100$

Subtask 2: (60 points)
$1 ≤ T ≤ 100$
$1 ≤ U, V ≤ 10^{9}$

----- Sample Input 1 ------
1
1 2
----- Sample Output 1 ------
8

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