You are given an $N\times N$ grid of complex numbers, all initially equal to $i$, the imaginary unit. A series of $Q$ updates will be made to the grid, in one of the following formats:

• R j - multiply every number in row $j$ by $i$.
• C j - multiply every number in column $j$ by $i$.
• I - increment every number in the grid by $i$.

After all $Q$ updates, determine the sum of the numbers in the grid.

Constraints

$1\le N,Q\le 5\times {10}^5$
$1\le j\le N$

Subtask 1 [30%]

There are no increment (type I) updates.

Subtask 2 [70%]

No additional constraints.

Input Specification

The first line contains two space-separated integers, $N$ and $Q$, the sidelength of the grid and the number of updates, respectively.

The next $Q$ lines each contain an update in one of the following formats:

• R j - multiply every number in row $j$ by $i$.
• C j - multiply every number in column $j$ by $i$.
• I - increment every number in the grid by $i$.

Output Specification

The sum of the numbers in the grid after all $Q$ updates can be expressed in the form $a+bi$, where $a$ and $b$ are integers. Output one line containing two space-separated integers, $a$ and $b$.

Note: These numbers may not fit within a 32-bit integer type.

Sample Input

5 4
R 3
I
C 1
R 4

Sample Output

-19 25

Explanation for Sample

Here is the state of the grid after each update:

Initially, every number in the grid is equal to $i$.

$\left[\begin{array}{ccccc}i& i& i& i& i\\ i& i& i& i& i\\ i& i& i& i& i\\ i& i& i& i& i\\ i& i& i& i& i\end{array}\right]$

The first update, R 3, multiplies every number in row $3$ by $i$.

$\left[\begin{array}{ccccc}\phantom{-}i& \phantom{-}i& \phantom{-}i& \phantom{-}i& \phantom{-}i\\ \phantom{-}i& \phantom{-}i& \phantom{-}i& \phantom{-}i& \phantom{-}i\\ -1& -1& -1& -1& -1\\ \phantom{-}i& \phantom{-}i& \phantom{-}i& \phantom{-}i& \phantom{-}i\\ \phantom{-}i& \phantom{-}i& \phantom{-}i& \phantom{-}i& \phantom{-}i\end{array}\right]$

The second update, I, increments every number in the grid by $i$.

$\left[\begin{array}{ccccc}\phantom{-}2i& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i\\ \phantom{-}2i& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i\\ -1+i& -1+i& -1+i& -1+i& -1+i\\ \phantom{-}2i& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i\\ \phantom{-}2i& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i\end{array}\right]$

The third update, C 1, multiplies every number in column $1$ by $i$.

$\left[\begin{array}{ccccc}-2& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i\\ -2& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i\\ -1-i& -1+i& -1+i& -1+i& -1+i\\ -2& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i\\ -2& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i\end{array}\right]$

The fourth update, R 4, multiplies every number in row $4$ by $i$.

$\left[\begin{array}{ccccc}-2& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i\\ -2& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i\\ -1-i& -1+i& -1+i& -1+i& -1+i\\ -2i& -2& -2& -2& -2\\ -2& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i& \phantom{-}2i\end{array}\right]$

Finally, the sum of all the numbers in the grid is $-19+25i$. Thus, $a=-19$ and $b=25$, and the correct output is -19 25.