#include<bits/stdc++.h>
#define int long long
#define mod 998244353ll
#define pii pair<int,int>
#define fi first
#define se second
#define mems(x,y) memset(x,y,sizeof(x))
#define pb push_back
#define db double
using namespace std;
const int maxn=3010;
const int inf=1e18;
inline int read(){
	int x=0,f=1;
	char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=(x<<3)+(x<<1)+(ch-48);ch=getchar();}
	return x*f;
}
bool Mbe;

int n,a[maxn],ans;
int pre[15]={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47};
inline int ksm(int a,int b=mod-2){
	int ans=1;
	while(b){
		if(b&1)ans=ans*a%mod;
		a=a*a%mod;
		b>>=1;
	}
	return ans;
}
vector<int> id[maxn];
int dp[1<<15],f[1<<15];
int msk[maxn];
void work(){
	n=read();
	for(int i=1;i<=n;i++)a[i]=read();
	for(int i=1;i<=n;i++){
		int x=a[i];
		for(int j=0;j<15;j++)if(x%pre[j]==0){
			msk[i]|=1<<j;
			while(x%pre[j]==0)x/=pre[j];
		}
		if(x==53*53)x=53;
		id[x].pb(i);
	}
	dp[0]=1;
	for(int i=1;i<=maxn-10;i++)if(id[i].size()){
		for(int j:id[i]){
			for(int s=(1<<15)-1;~s;s--){
				(f[s|msk[j]]+=f[s]*(i==1?a[j]:a[j]/i*(i-1))+dp[s]*a[j])%=mod;
			}
		}
		for(int s=0;s<(1<<15);s++)(dp[s]+=f[s])%=mod;
	}
	for(int s=0;s<(1<<15);s++)if(dp[s]){
		int val=dp[s];
		for(int i=0;i<n;i++)if(s&(1<<i)){
			val=val*ksm(pre[i])%mod*(pre[i]-1)%mod;
		}
		// cout<<s<<" "<<dp[s]<<" "<<val<<"\n";
		(ans+=val)%=mod;
	}
	printf("%lld\n",ans);
}

// \
444

bool Med;
int T;
signed main(){
//	freopen(".in","r",stdin);
//	freopen(".out","w",stdout);
	
//	ios::sync_with_stdio(0);
//	cin.tie(0);cout.tie(0);
	
//	cerr<<(&Mbe-&Med)/1048576.0<<" MB\n";
	
	T=1;
	while(T--)work();
}