Gcd Sum

$G (N) = \sum_{j = 1}^{N} \sum_{i = 1}^{j} gcd (i, j)$ .
You are given: $G (10) = 122$ .

Find $G (10^{11})$ . Give your answer modulo $998244353$ .

Write-up coming later

The complete problem is available here. An approach, code, and answer will be added later.