Once you implement the function \(f\) that evaluates \(f(x)\) for any given \(x\), all that left is to iteratively compute \(A_0, A_1, \ldots, A_N\) to find the answer.

The approaches to implement \(f\) include: repeatedly finding the remainder when \(x\) is divided by \(10\) and then dividing it by \(10\), or converting \(x\) it into a string.

Sample code

#include <bits/stdc++.h>
using namespace std;

int main() {
	int n;
	cin >> n;

	auto f = [&](int x) -> int {
		int res = 0;
		while (x) {
			res += x % 10;
			x /= 10;
		}
		return res;
	};

	vector<int> a(n + 1);
	a[0] = 1;
	for (int i = 1; i <= n; i++) {
		for (int j = 0; j < i; j++) a[i] += f(a[j]);
	}
	cout << a[n] << '\n';
}