Submission #4298388

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Source Code Expand

/*input
10
1
10
100
1000000007
10000000000
1000000009
999999999
999
999
999
*/
#include <bits/stdc++.h>
#pragma GCC optimize("unroll-loops,no-stack-protector")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef pair<double,double> pdd;
#define IOS ios_base::sync_with_stdio(0); cin.tie(0)
#define ALL(a) a.begin(),a.end()
#define SZ(a) ((int)a.size())
#define F first
#define S second
#define REP(i,n) for(int i=0;i<((int)n);i++)
#define pb push_back
#define MP(a,b) make_pair(a,b)
#define SORT_UNIQUE(c) (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
#define GET_POS(c,x) (lower_bound(c.begin(),c.end(),x)-c.begin())
template<typename T1,typename T2>
ostream& operator<<(ostream& out,pair<T1,T2> P){
	out<<'('<<P.F<<','<<P.S<<')';
	return out;
}

//}}}
const ll maxn=100005;
const ll maxlg=__lg(maxn)+2;
const ll INF64=8000000000000000000LL;
const int INF=0x3f3f3f3f;
const ll MOD=ll(1e9+7);
const double PI=acos(-1);
//const ll p=880301;
//const ll P=31;

ll mypow(ll a,ll b){
	ll res=1LL;
	while(b){
		if(b&1) res=res*a%MOD;
		a=a*a%MOD;
		
		b>>=1;
	}
	return res;
}

vector<ll> p;
bool isp[maxn];

map<ll,ll> mp;

ll a[maxn];

ll nocube(ll x){
	for(ll i:p){
		if(i*i*i>x) break;
		while(x%(i*i*i)==0) x/=(i*i*i);
	}
	return x;
}

map<ll,ll> cnt;

set<ll> vis;
int main()
{
	IOS;

	for(int i=2;i<maxn;i++){
		if(!isp[i]) p.pb(i);
		for(int j=0;i*p[j]<maxn;j++){
			isp[i*p[j]]=0;
			if(i%p[j]==0) break;
		}
	}
	for(ll i:p){
		if(i*i*i>1000000000LL){
			ll d=i*i;
			for(ll j=d;j<maxn;j+=d) mp[d]=i;
		}
	}

	int n;
	cin>>n;
	REP(i,n) cin>>a[i];
	REP(i,n) a[i]=nocube(a[i]);
	// REP(i,n) cout<<a[i]<<" \n"[i==n-1];
	bool flag=0;
	REP(i,n){
		if(a[i]>1) cnt[a[i]]++;
		else flag=1;
	}
	ll ans=0;
	for(auto i:cnt){
		ll type=i.F;
		if(vis.count(type)) continue;
		vis.insert(type);
		__int128 tmp=type*type;
		if(mp.count(type)){
			ll pp=mp[type];
			tmp/=pp*pp*pp;
		}
		for(ll i:p){
			if(i*i*i>10000000000LL) break;

			while(type%(i*i)==0) tmp/=(i*i*i);
		}
		// cout<<type<<' '<<(ll)tmp<<'\n';
		if(tmp<10000000005LL&&cnt.count((ll)tmp)){
			ans+=max(i.S,cnt[tmp]);
			vis.insert(tmp);
		}
		else ans+=i.S;
	}
	cout<<ans+flag<<'\n';
	return 0;
}

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