Link is playing nim game with fried-chicken. If you don't know this game, here're the rules:

There are two players in this game, called Alice and Bob. The game starts with  piles of stones, the -th pile contains  stones.

Alice and Bob take turns to play this game, Alice goes first. In each turn, the player should choose one pile of stones, and remove  stones from that pile. The player who can not operate loses.

Obviously, one of Alice and Bob has a winning strategy. If one player has a winning strategy, he or she wants to win in minimum turns. If one player will lose, he or she wants to lose in maximum turns.

Now, fried-chicken wonders, when both players uses the best strategy:

How many turns will take before the game ends?

How many kinds of operations can Alice do in the first turn under the restrictions above?

Each test contains multiple test cases. The first line contains the number of test cases . Description of the test cases follows.

The first line contains a single integer .

The second line contains  integers .

It is guaranteed that the sum of  over all test cases does not exceed .

For each test case, output two integers in one line, which are the turns taken before the game ends and the kinds of operation Alice can do in the first turn under the restrictions above.

6
1
1
1
2
2
1 1
3
1 2 3
6
1 1 4 5 1 4
6
1 9 1 9 8 10

1 1
1 1
2 2
6 2
13 3
37 1