import java.util.Scanner;
public class Main{
public static boolean isprimes(int n){
if(n < 2 ) return false;
for(int i = 2; i <= n/i; i++){
if(n % i == 0) return false;
}
return true;
}
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
while(n-- > 0){
int x = sc.nextInt();
if(isprimes(x)){
System.out.println("Yes");
}else{
System.out.println("No");
}
}
}
}
import java.util.Scanner;
public class Main{
public static void fun(int n){
for(int i = 2; i <= n/i;i++){
if(n % i==0){
int res = 0;
while(n % i ==0){
n/=i;
res++;
}
System.out.printf("%d %d\n",i,res);
}
}
if(n > 2) System.out.printf("%d %d\n",n,1);
System.out.println();
}
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
while(n-- > 0){
int x = sc.nextInt();
fun(x);
}
}
}
import java.util.Scanner;
public class Main{
static int idx = 0;
static int N = 1000010;
static int[] primes = new int[N];
static boolean[] st =new boolean[N];
public static void get_primes(int n){
for(int i = 2; i <= n; i++){
if(!st[i]) primes[idx++] = i;
for(int j = 0; primes[j] <= n / i; j++){
st[primes[j] * i] = true;
if(i % primes[j] == 0) break;
}
}
}
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
get_primes(n);
System.out.println(idx);
}
}
import java.util.Scanner;
import java.util.HashMap;
public class Main{
static HashMap<Integer,Integer> primes = new HashMap<>();
static long res ;
static int mod = (int)1e9 + 7;
public static void getNums(int n){
for(int i = 2; i <= n / i;i++){
while(n % i == 0){
n /= i;
primes.put(i, primes.getOrDefault(i,0) + 1);
}
}
if( n > 2) primes.put(n,primes.getOrDefault(n,0) + 1);
}
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
while( n-- > 0){
int x = sc.nextInt();
getNums(x);
}
res = 1;
for(int a: primes.values()){
res = res * (a + 1) % mod;
}
System.out.println(res);
}
}
import java.util.Scanner;
import java.util.HashMap;
public class Main{
static int mod = (int)1e9 + 7;
static int N = 110;
static HashMap<Integer,Integer> primes = new HashMap<>();
public static void getNums(int n){
for(int i = 2; i <= n / i;i++){
while(n % i == 0){
n /=i;
primes.put(i,primes.getOrDefault(i,0) + 1);
}
}
if( n > 1) primes.put(n, primes.getOrDefault(n,0) + 1);
}
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
while( n-- > 0){
int x = sc.nextInt();
getNums(x);
}
long res = 1;
for(Integer a: primes.keySet()){
long t = 1;
int k = primes.get(a);
while(k-- != 0){
t = (t * a + 1) % mod;
}
res = t * res % mod;
}
System.out.println(res);
}
}
import java.util.Scanner;
public class Main{
public static int gcd(int a,int b){
if(b!= 0){
return gcd(b,a % b);
}else{
return a;
}
}
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
while( n-- > 0){
int a = sc.nextInt();
int b = sc.nextInt();
System.out.println(gcd(a,b));
}
}
}
import java.util.Scanner;
public class Main{
static long res;
public static void eulers(int n){
res = n;
for(int i = 2; i <= n/i; i++){
if(n % i==0){
while(n % i == 0){
n /= i;
}
res = res / i * (i - 1);
}
}
if( n > 1) res = res / n * (n - 1);
System.out.println(res);
}
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
while(n-- > 0){
int x = sc.nextInt();
eulers(x);
}
}
}
import java.util.Scanner;
public class Main{
static int N = 1000010;
static int[] primes = new int[N];
static boolean[] st = new boolean[N];
static int idx = 0;
static int[] phi = new int[N];
static long res = 0;
public static void get_eulers(int n ){
phi[1] = 1;
for(int i = 2; i <= n; i++){
if(!st[i]){
primes[idx++] = i;
phi[i] = i - 1;
}
for(int j = 0; primes[j] <= n/i;j++){
st[primes[j] * i] = true;
if(i % primes[j] == 0){
phi[primes[j] * i] = primes[j] * phi[i];
break;
}
phi[primes[j] * i] = phi[i] * (primes[j] - 1);
}
}
for(int a: phi){
res += a;
}
System.out.println(res);
}
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
get_eulers(n);
}
}
import java.util.Scanner;
public class Main{
static int N = 100010;
static long res = 1;
public static long qmi(long a,int k,int p){
res = 1;
while(k!=0){
if((k & 1) != 0) res = res * a % p;
k >>= 1;
a = a * a % p;
}
return res;
}
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
while(n-- > 0){
int a = sc.nextInt();
int b = sc.nextInt();
int k = sc.nextInt();
System.out.println(qmi(a,b,k));
}
}
}
import java.util.Scanner;
public class Main{
public static long qmi(long a,int k,int p){
long res = 1;
while(k != 0){
if((k & 1) != 0) res = res * a % p;
k >>= 1;
a = a * a % p;
}
return res;
}
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
while(n-- > 0){
int a = sc.nextInt();
int p = sc.nextInt();
if( a % p != 0){
System.out.println(qmi(a, p - 2, p));
}else{
System.out.println("impossible");
}
}
}
}
import java.util.Scanner;
public class Main{
static int N = 2010;
static int[][] c = new int[N][N];
static int mod = (int)1e9 + 7;
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
for(int i = 0; i < N;i++){
for(int j = 0; j <= i;j++){
if(j == 0){
c[i][j] = 1;
}else{
c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod;
}
}
}
while(n-- > 0){
int a = sc.nextInt();
int b = sc.nextInt();
System.out.println(c[a][b]);
}
}
}
import java.util.Scanner;
public class Main{
static int N = 100010;
static long[] fact = new long[N];
static long[] infact = new long[N];
static int mod = (int) 1e9 + 7;
public static long qmi(long a,int k,int p){
long res = 1;
while(k != 0){
if((k & 1) != 0) res = res * a % p;
k >>= 1;
a = a * a % p;
}
return res;
}
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
fact[0] = infact[0] = 1;
for(int i = 1; i < N;i++){
fact[i] = fact[i - 1] * i % mod;
infact[i] = infact[i - 1] * qmi(i,mod - 2,mod) % mod;
}
while(n-- > 0){
int a = sc.nextInt();
int b = sc.nextInt();
System.out.println(fact[a] * infact[a - b] % mod * infact[b] % mod);
}
}
}
