You are given $$$n$$$ segments on the coordinate axis. The $$$i$$$-th segment is $$$[l_i, r_i]$$$. Let's denote the set of all integer points belonging to the $$$i$$$-th segment as $$$S_i$$$.
Let $$$A \cup B$$$ be the union of two sets $$$A$$$ and $$$B$$$, $$$A \cap B$$$ be the intersection of two sets $$$A$$$ and $$$B$$$, and $$$A \oplus B$$$ be the symmetric difference of $$$A$$$ and $$$B$$$ (a set which contains all elements of $$$A$$$ and all elements of $$$B$$$, except for the ones that belong to both sets).
Let $$$[\mathbin{op}_1, \mathbin{op}_2, \dots, \mathbin{op}_{n-1}]$$$ be an array where each element is either $$$\cup$$$, $$$\oplus$$$, or $$$\cap$$$. Over all $$$3^{n-1}$$$ ways to choose this array, calculate the sum of the following values:
$$$$$$|(((S_1\ \mathbin{op}_1\ S_2)\ \mathbin{op}_2\ S_3)\ \mathbin{op}_3\ S_4)\ \dots\ \mathbin{op}_{n-1}\ S_n|$$$$$$
In this expression, $$$|S|$$$ denotes the size of the set $$$S$$$.
The first line contains one integer $$$n$$$ ($$$2 \le n \le 3 \cdot 10^5$$$).
Then, $$$n$$$ lines follow. The $$$i$$$-th of them contains two integers $$$l_i$$$ and $$$r_i$$$ ($$$0 \le l_i \le r_i \le 3 \cdot 10^5$$$).
Print one integer — the sum of $$$|(((S_1\ \mathbin{op}_1\ S_2)\ \mathbin{op}_2\ S_3)\ \mathbin{op}_3\ S_4)\ \dots\ \mathbin{op}_{n-1}\ S_n|$$$ over all possible ways to choose $$$[\mathbin{op}_1, \mathbin{op}_2, \dots, \mathbin{op}_{n-1}]$$$. Since the answer can be huge, print it modulo $$$998244353$$$.
4 3 5 4 8 2 2 1 9
162
4 1 9 3 5 4 8 2 2
102
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