CF1400G.Mercenaries

Polycarp plays a (yet another!) strategic computer game. In this game, he leads an army of mercenaries.

Polycarp wants to gather his army for a quest. There are $n$ mercenaries for hire, and the army should consist of some subset of them.

The $i$-th mercenary can be chosen if the resulting number of chosen mercenaries is not less than $l_i$ (otherwise he deems the quest to be doomed) and not greater than $r_i$ (he doesn't want to share the trophies with too many other mercenaries). Furthermore, $m$ pairs of mercenaries hate each other and cannot be chosen for the same quest.

How many non-empty subsets does Polycarp need to consider? In other words, calculate the number of non-empty subsets of mercenaries such that the size of this subset belongs to $[l_i, r_i]$ for each chosen mercenary, and there are no two mercenaries in the subset that hate each other.

The answer may be large, so calculate it modulo $998244353$.

波利卡普正在玩一款（又一款！）策略类电脑游戏。在这款游戏中，他率领一支雇佣兵军队。

波利卡普希望为一次任务集结他的军队。目前有 $n$ 名可雇佣的雇佣兵，而军队应由其中某个子集构成。

第 $i$ 名雇佣兵可以被选中，当且仅当最终被选中的雇佣兵总数不小于 $l_i$（否则他认为该任务注定失败），且不大于 $r_i$（他不愿与过多其他雇佣兵分享战利品）。此外，还有 $m$ 对雇佣兵彼此憎恨，不能同时被选入同一支任务队伍。

波利卡普需要考虑多少个非空子集？换言之，请计算满足如下条件的非空雇佣兵子集的数目：对子集中每个被选中的雇佣兵 $i$，该子集的大小均属于区间 $[l_i, r_i]$；且子集中不存在一对彼此憎恨的雇佣兵。

答案可能很大，请对 $998244353$ 取模。

The first line contains two integers $n$ and $m$ ($1 \le n \le 3 \cdot 10^5$, $0 \le m \le \min(20, \dfrac{n(n-1)}{2})$) — the number of mercenaries and the number of pairs of mercenaries that hate each other.

Then $n$ lines follow, the $i$-th of them contains two integers $l_i$ and $r_i$ ($1 \le l_i \le r_i \le n$).

Then $m$ lines follow, the $i$-th of them contains two integers $a_i$ and $b_i$ ($1 \le a_i \lt b_i \le n$) denoting that the mercenaries $a_i$ and $b_i$ hate each other. There are no two equal pairs in this list.

第一行包含两个整数 $n$ 和 $m$（$1 \le n \le 3 \cdot 10^5$，$0 \le m \le \min(20, \dfrac{n(n-1)}{2})$）—— 分别表示雇佣兵人数以及相互憎恨的雇佣兵对数。

接下来 $n$ 行，其中第 $i$ 行包含两个整数 $l_i$ 和 $r_i$（$1 \le l_i \le r_i \le n$）。

接下来 $m$ 行，其中第 $i$ 行包含两个整数 $a_i$ 和 $b_i$（$1 \le a_i \lt b_i \le n$），表示雇佣兵 $a_i$ 和 $b_i$ 相互憎恨。该列表中不存在重复的数对。

Print one integer — the number of non-empty subsets meeting the constraints, taken modulo $998244353$.

输出一个整数——满足约束条件的非空子集的数量，对 $998244353$ 取模。