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Cod sursa(job #978733)
#include<stdio.h>
#include<math.h>
#include<cstring>
#define maxd 1000005
#define maxp 80000
#define mod 9973
using namespace std;
typedef long long ll;
int t,p,nrd;
int prime[maxp];
ll n,sum;
bool sieve[maxd];
void preproc()
{
int i,lim=maxd-5;
prime[++p]=2;
for(i=3;i*i<=lim;i+=2)
if(!sieve[i])
{
prime[++p]=i;
for(int j=i;i*j<=lim;j++)
sieve[i*j]=true;
}
for(;i<=lim;i+=2)
if(!sieve[i])
prime[++p]=i;
}
void gcd(int a,int b,ll &x,ll &y)
{
if(b==0) {x=1; y=0; return;}
ll x0,y0;
gcd(b,a%b,x0,y0);
x=y0;
y=x0-a/b*y0;
}
ll modular(int a,int b)
{
ll x,y;
gcd(a,b,x,y);
while(x<0) x+=mod;
return x;
}
void update(int nr,ll prod,ll x)
{
nrd*=(nr+1);
sum=(sum*((prod-1)%mod))%mod;
sum=(sum*x)%mod;
}
void solve()
{
int nr;
ll sq,prod,inv;
scanf("%d",&t);
for(int i=1;i<=t;i++)
{
scanf("%lld",&n);
sq=sqrt(n); nrd=1; sum=1;
for(int j=1;prime[j]<=sq;j++)
if(n%prime[j]==0)
{
inv=modular(prime[j]-1,mod);
nr=0; prod=prime[j]%mod;
while(n%prime[j]==0)
{
nr++;
prod=(prod*(prime[j]%mod))%mod;
n/=prime[j];
}
update(nr,prod,inv);
}
if(n>1)
{
inv=modular(n-1,mod);
prod=( (n%mod)*(n%mod) )%mod;
update(1,prod,inv);
}
printf("%d %lld\n",nrd,sum);
}
}
int main()
{
freopen("ssnd.in","r",stdin);
freopen("ssnd.out","w",stdout);
preproc();
solve();
fclose(stdin);
fclose(stdout);
return 0;
}