#include <bits/stdc++.h>
#define rep(i,j,k) for(int i=j;i<=(k);++i)
#define mod 998244353
#define MAXN 2005
typedef long long ll;
int n,rk,pri[MAXN],state[MAXN];
std::pair<int,int> a[MAXN];
ll ans,val[1<<16],f[1<<16],g[1<<16],tmp[1<<16];
inline bool chk(int x){
	rep(i,2,x-1) if(x%i==0) return false;
	return true;
}
inline void init(){
	rep(i,2,53) if(chk(i)) pri[++rk]=i;
}
inline ll pw(int x,int y){
	ll base=x,ret=1;
	for(;y;y>>=1,(base*=base)%=mod) if(y&1) (ret*=base)%=mod;
	return ret;
}
int main(){
	std::ios::sync_with_stdio(0);
	std::cin.tie(0),std::cout.tie(0);
	std::cin>>n,init();
	rep(i,1,n) std::cin>>a[i].first,a[i].second=a[i].first;
	rep(i,1,n){
		rep(j,1,rk) if(a[i].first%pri[j]==0){
			state[i]|=1<<(j-1);
			while(a[i].first%pri[j]==0) a[i].first/=pri[j];
		}
	}
	rep(s,0,(1<<rk)-1){
		val[s]=1;
		rep(i,1,rk) if((s>>(i-1))&1) val[s]=val[s]*(pri[i]-1)%mod*pw(pri[i],mod-2)%mod;
	}
	std::sort(a+1,a+n+1),f[0]=1;
//	rep(i,1,n) std::cerr<<a[i].first<<' '<<a[i].second<<'\n';
	rep(i,0,n-1){
		int cur=i+1;
		while(a[cur+1].first==a[cur].first) ++cur;
		rep(s,0,(1<<rk)-1) tmp[s]=f[s];
		rep(j,i+1,cur){
			rep(s,0,(1<<rk)-1) g[s]=f[s];
			rep(s,0,(1<<rk)-1) f[s|state[j]]=(f[s|state[j]]+g[s]*a[j].second%mod*val[(s|state[j])^s])%mod;
		} 
//		rep(s,0,(1<<rk)-1) if(f[s]) std::cerr<<i<<' '<<s<<' '<<f[s]<<'\n';
        if(a[i+1].first>1){
        	rep(s,0,(1<<rk)-1) g[s]=f[s];
		    rep(s,0,(1<<rk)-1) f[s]=((g[s]-tmp[s]+mod)*(a[i+1].first-1)%mod*pw(a[i+1].first,mod-2)+tmp[s])%mod;
		}
		i=cur-1;
//		rep(s,0,(1<<rk)-1) if(f[s]) std::cerr<<i<<' '<<s<<'\n';
	} 
	rep(s,0,(1<<rk)-1) ans+=f[s];
	std::cout<<ans%mod<<'\n';
}