#include <bits/stdc++.h>
#define ll long long
using namespace std;
constexpr int mod=998244353;
int isprime[3005],prime[3000],cnt;
vector<int> use[3005];
int inv[3005];
void paralysis(){
	for (int i=2;i<=3000;i++){
		if (!isprime[i]) prime[++cnt]=i;
		for(int j=1;j<=cnt&&i*prime[j]<=3000;j++){
			isprime[i*prime[j]]=1;
			if (i%prime[j]==0){
				break;
			}
		}
	}
	vector<int> p;
	for (int i=2;i<=53;i++){
		if (!isprime[i]){
			p.push_back(i);
		}
	}
	
	int n;
	cin>>n;
	vector<int> a(n+1);
	for (int i=1;i<=n;i++){
		cin>>a[i];
	}
	
	for (int i=1;i<=n;i++){
		int now=a[i];
		for (auto x:p){
			while (now%x==0){
				now/=x;
			}
		}
		use[now].push_back(a[i]);
	}
	
	vector<int> f(1<<16);
	f[0]=1;
	for (auto x:use[1]){
		int mask=0;
		for (int i=0;i<p.size();i++){
			if (x%p[i]==0){
				mask|=(1<<i);
			}
		}
		
		auto res=f;
		for (int i=0;i<(1<<16);i++){
			f[i|mask]=(f[i|mask]+1LL*res[i]*x%mod)%mod;
		}
	}
	
	for (int i=54;i<=3000;i++){
		if (use[i].size()==0) continue;
		vector<vector<int>> dp(2,vector<int>(1<<16));
		dp[0]=f;
		for (auto x:use[i]){
			auto res=dp;
			int mask=0;
			for (int j=0;j<p.size();j++){
				if (x%p[j]==0){
					mask|=(1<<j);
				}
			}
			
			for (int j=0;j<(1<<16);j++){
				dp[1][j|mask]=(dp[1][j|mask]+1LL*res[0][j]*x%mod)%mod;
			}
		}
		for (int j=0;j<(1<<16);j++){
			f[j]=(dp[0][j]+1LL*dp[1][j]*(i-1)%mod*inv[i-1]%mod)%mod;
		}
	}
	
	int ans=0;
	for (int i=0;i<(1<<16);i++){
		int s=1;
		for (int j=0;j<16;j++){
			if (i>>j&1){
				s=1LL*s*(p[j]-1)%mod*inv[p[j]]%mod;
			}
		}
		ans=(ans+1LL*f[i]*s%mod)%mod;
	}
	cout<<ans<<"\n";
}
/*
3
1 2 3
*/
signed main()
{
	ios::sync_with_stdio(0);
    cin.tie(0);
    
    for (int i=1;i<=3000;i++){
        inv[i]=(i==1?1:1LL*(mod-mod/i)*inv[mod%i]%mod);
    }

    
    int t=1;
//    cin>>t;
	while (t--){
		paralysis();
	}
	return 0;
}