cf1033D

 

每一个数都是 p*q p^2 p^3 p^4 的形式，分类讨论即可

 

#include<bits/stdc++.h>
#define forn(i, n) for (int i = 0 ; i < int(n) ; i++)
#define fore(i, s, t) for (int i = s ; i < (int)t ; i++)
#define fi first
#define se second
#define all(x) x.begin(),x.end()
#define pf2(x,y) printf("%d %d\n",x,y)
#define pf(x) printf("%d\n",x)
#define each(x) for(auto it:x)  cout<<it<<endl;
#define pii pair<int,int>
#define sc(x) scanf("%d",&x)
using namespace std;
typedef long long ll;
const int maxn=2e5+5;
const int maxm=2e5+5;
const int inf=1e9;
const ll mod=998244353;
ll a[maxn],n;


long long my_sqrt(long long x) {
	long long l=1,r=2e9;
	while(l<r){
		long long mid=(l+r+1)>>1;
		if(mid*mid<=x) l=mid;
		else r=mid-1;
	}
	return l;
}
long long my_crt(long long x) {
	assert(x > 0);
	long long y = (long long) (powl((long double) x, 1.0 / 3.0) + 0.5);
	while (y * y * y<x) y++;
	while (y * y * y>x) y--;
	if (y * y * y == x) {
		return y;
	}
	return -1;
}
int main() {
	cin>>n;
	for(int i=0;i<n;i++)
		cin>>a[i];
	map<ll,vector<pair<ll,ll>>> ls;
	ll ans=1;
	map<ll,ll> eq;
	for(int i=0;i<n;i++){
		ll t=my_sqrt(a[i]);
		if(t*t==a[i]) {
			ll k=my_sqrt(t);
			if(k*k*k*k==a[i]) ls[i].push_back({k,4});
			else ls[i].push_back({t,2}); 
		}
		else {
			t=my_crt(a[i]);
			if(t*t*t==a[i]) {
				ls[i].push_back({t,3});
			}
			else {
				bool flag=0;
				for(int j=0;j<n;j++){
					if(j==i || a[i] == a[j])  continue;
					ll g=__gcd(a[i],a[j]);
					if(g!=1) {
						ls[i].push_back({g,1});
						ls[i].push_back({a[i]/g,1});
						flag=1;break;
					}
				}
				if(!flag) {
					eq[a[i]]++;
				}
			}
			
		}
	}
	for(auto i:eq)
		if(i.se==1) ans=ans*4%mod;
		else ans=ans*(i.se+1)%mod*(i.se+1)%mod;
	map<ll,ll> ct;
	for(auto i:ls)
		for(auto j:i.se)
			ct[j.fi]+=j.se;
	for(auto i:ct)
		ans=ans*(i.se+1)%mod;
	cout<<ans<<endl;
}