Statement

After Timothy from the Department of Mathematics completed his study of real analysis over $\mathbb{R}$, he started to take complex analysis in the next semester.

All prerequisites for complex analysis stem from the extension of the number field, specifically the equation $\mathrm{i}^2=-1$. Negative numbers, on the other hand, consist of two parts: a real part $a$ and an imaginary part $b$. In simple terms, a complex number can be represented as $a+b\mathrm{i}$, where $a$ and $b$ are both real numbers. The multiplication on $\mathbb{C}$ is defined as $(a+b\mathrm{i})(c+d\mathrm{i})=(ac-bd)+(cb+ad)\mathrm{i}$, resulting in a new real part $ac-bd$ and an imaginary part $cb+ad$.

Given $n$ complex numbers of the form $a+b\mathrm{i}$, define the product of these $n$ complex numbers as $x+y\mathrm{i}$. Please try to find the values of $x$ and $y$ respectively. Since the result may be very large, please output the answer modulo 998244353.

To ensure that the result of the modulo operation remains positive, we redefine the modulo operation as follows: For any integer $a$ and a non-zero integer $m$, there exists a unique pair of integers $q$ and $r$ that simultaneously satisfy the following two conditions:

1. $a=q\times m+r$;
2. $0\leqslant r < |m|$

The result of the modulo operation at this time is denoted as $a~\% ~m=r$, for example, $-22~\% ~30=8, 20~\% ~3=2$.

Input

Input a single integer $n$ in the first line, satisfying $1\leqslant n\leqslant 2\times 10^5$, representing the number of complex numbers.

In the following $n$ lines, each line contains two integers $a_i, b_i$ representing a complex number, where $-1\times 10^9 \leqslant a_i, b_i \leqslant 1\times 10^9$.

Output

Output two non-negative integers representing the values of $x$ and $y$ modulo 998244353, respectively.

Samples

3
1 1
4 5
1 4

998244316 5

5
114514 1919810
114 514
1 1
4 5
1 4

699025846 827685096