13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T6ad,

You are given a multiset $$$S$$$. Over all pairs of subsets $$$A$$$ and $$$B$$$, such that:

$$$B \subset A$$$;
$$$|B| = |A| - 1$$$;
greatest common divisor of all elements in $$$A$$$ is equal to one;

find the sum of $$$\sum_{x \in A}{x} \cdot \sum_{x \in B}{x}$$$, modulo $$$998\,244\,353$$$.

Input

The first line contains one integer $$$m$$$ ($$$1 \le m \le 10^5$$$): the number of different values in the multiset $$$S$$$.

Each of the next $$$m$$$ lines contains two integers $$$a_i$$$, $$$freq_i$$$ ($$$1 \le a_i \le 10^5, 1 \le freq_i \le 10^9$$$). Element $$$a_i$$$ appears in the multiset $$$S$$$ $$$freq_i$$$ times. All $$$a_i$$$ are different.

Output

Print the required sum, modulo $$$998\,244\,353$$$.

Note

A multiset is a set where elements are allowed to coincide. $$$|X|$$$ is the cardinality of a se

Sum Over Subsets

Examples