Few of my friends are working on a game called “Move It!”. It's a tile-based game played on an $n\times n$ square grid. Each square can either be empty or contain an object (a rock or a fruit).

The player starts from the top-left corner of the grid. If a player is in square $(i, j)$, he/she can only move to square $(i+1, j)$ or $(i, j+1)$ in one move. However, if any square contains a rock, the player cannot move to that grid. If any square contains fruit, the player can collect the fruit by moving to that square. The goal is to reach the bottom-right corner of the grid while collecting as many fruits as possible.

My friends already built a demo version of the game and gave it to me to test it. To test the game thoroughly, I want to explore as many paths as possible that I can take to reach the goal by collecting the maximum possible amount of fruits.

It is guaranteed that the top-left corner and the bottom-right corner squares will be empty.

Input

The first line of the input will contain a single integer $t (1 \leq t \leq 10)$, the number of test cases.

For each test case, there will be one integer $n (1 \leq n \leq 1000)$, the side-length of the square grid. The following $n$ lines each will contain $n$ characters. The characters can either be:

. denoting an empty square.

r denoting a rock.

f denoting a fruit.

Output

If it's not possible to reach the goal, print $-1$. Otherwise, print two space-separated integers denoting the maximum number of fruits I can collect to reach the goal and the possible number of paths that I can use to reach the goal while collecting that many fruits.

As the possible number of paths can be huge, print the count modulo $10^9+7$.