#include<bits/stdc++.h>
#define int long long
#define fr(i,j,k) for(register int i=j;i<=k;++i)
#define rf(i,j,k) for(register int i=j;i>=k;--i)
#define foredge(i,j) for(register int i=head[j];i;i=e[i].nxt)
#define randfind(l,r) (rand()%((r)-(l)+1)+(l))
#define pb push_back
#define Times printf("Time:%.3lf\n",clock()/CLOCKS_PER_SEC)
using namespace std;
inline int read(){
	int x=0;
	bool f=0;
	char c=getchar();
	while(!isdigit(c)) f|=(c=='-'),c=getchar();
	while(isdigit(c)) x=(x<<3)+(x<<1)+(c^48),c=getchar();
	return f?-x:x;
}
inline void write(int x){
    if(x<0){putchar('-');x=-x;}
    if(x>9)write(x/10);
    putchar(x%10+'0');
}
inline void writeln(int x){write(x); puts("");}
inline void writepl(int x){write(x); putchar(' ');}
//inline void init(){
//	int t=read();
//	while(t--) work();
//}
const int Maxn=1e5+10,mod=998244353;
vector<int> vc[Maxn];
int a[Maxn];
int n;
map<int,int> mp;
int cnt;
inline void init(){
    n=read();
    fr(i,1,n) a[i]=read();
}
int ans1=1;
inline void add(int x,int id){
    for(register int i=2;i*i<=x;++i){
        if(x%i!=0) continue;
        if(!mp[i]) mp[i]=++cnt;
        int tot;
        tot=mp[i];
        int pop=0;
        while(x%i==0) ++pop,x/=i;
        ans1*=((pop+2)*(pop+1)/2)%mod;ans1%=mod;
        vc[tot].push_back(pop);
    }
    if(x!=1){
        if(!mp[x]) mp[x]=++cnt;
        int tot=mp[x];
        ans1*=3,ans1%=mod;
        vc[tot].push_back(1);
    }
}
int f[Maxn],g[Maxn],g1[Maxn];
int ans2=1,nowsum;
inline int getsum(int x){return nowsum+x;}
inline void into(int x){
    vector<int> now;
    now=vc[x];
    for(register int i=0;i<now.size();++i) nowsum+=now[i];
    memset(f,0,sizeof(f));
    f[getsum(0)]=1;
    int tot=0;
    for(register int i=0;i<now.size();++i){
        // memset(g,0,sizeof(g));
        int x=now[i];
        fr(i1,0,x) fr(i2,0,i1) g1[getsum(2*i2-i1)]++;
        fr(j,-tot,tot) fr(k,-x,x) g[getsum(j+k)]+=f[getsum(j)]*g1[getsum(k)],g[getsum(j+k)]%=mod;
        fr(j,-x,x) g1[getsum(j)]=0;
        tot+=x;
        fr(j,-tot,tot) f[getsum(j)]=g[getsum(j)],g[getsum(j)]=0;
    }
    ans2*=f[getsum(0)],ans2%=mod;
}
inline int ksm(int x,int y){
    int sum=1;
    while(y){
        if(y&1) sum=sum*x%mod;
        x=x*x%mod;
        y=y/2;
    }
    return sum;
}
inline void work(){
    fr(i,1,n) add(a[i],i);
    fr(i,1,cnt) into(i);
    // writepl(ans1),writeln(ans2);
    // writeln(ksm(2,mod-2));
    writeln((ans1+ans2)*ksm(2,mod-2)%mod);
}
signed main(){
	// freopen("input.in","r",stdin);
	// freopen("output.out","w",stdout);
    init();work();
    // printf("\nTIME:%.3lf",(double)clock()/CLOCKS_PER_SEC);
	return 0;
}