Tara was completing an Algorithms assignment and got stuck on a question. She thought of who can help her, and got reminded of Kabir who has good problem solving skills. The question is:
Given N$N$ the number of elements in the sequence A1$A_1$,A2$A_2$ … An$A_n$. Find out the prime factor which occurred maximum number of times among the largest prime factor corresponding to each element. if there are more than one such prime factors print the largest one.
You are friends with Kabir, help him to solve the problem for Tara.

-----Input:-----
- The first line of the input contains a single integer T$T$ denoting the number of test cases. The description of T test cases follows. 
- First line of each test case contains N$N$, the number of elements in the sequence.
- Second line contains N space separated elements A1$A_1$,A2$A_2$ … An$A_n$.

-----Output:-----
- For each test case, print a single line, the number which occurs maximum number of times from the largest prime factor corresponding to each element.

-----Constraints-----
- 1≤T≤10$1 \leq T \leq 10$
- 1≤N≤105$1 \leq N \leq 10^5$
- 2≤A[i]≤105$2 \leq A[i] \leq 10^5$

-----Sample Input:-----
1
7

3 2 15 6 8 5 10

-----Sample Output:-----
5

-----EXPLANATION:-----
The largest prime factors of numbers are:
3 2  5  3  2  5  5 , of which 5 is most frequent.

Difficulty: interview

Starter code:

Solutions:
# cook your dish here
store=[0]*(10**5+1)
def sieve():
	for i in range(2,10**5+1):
		if(store[i]==0):
			store[i]=1
			for j in range(i,10**5+1,i):
				store[j]=i
sieve()
# print(store)
for _ in range(int(input())):
	
	n=int(input())
	li=[int(x) for x in input().split()]

	dp=[0]*(10**5+1)
	for i in li:
		dp[store[i]]+=1
	max_re=0
	res=0
	for i in li:
		if(dp[store[i]]==max_re):
			if(store[i]>res):
				res=store[i]
		elif(dp[store[i]]>max_re):
			max_re=dp[store[i]]
			res=store[i]
	
	print(res)





# cook your dish here
"""def power(x, y): 
    res = 1
    x=x
    while (y > 0): 
        if ((y & 1) == 1) : 
            res = (res * x) 
        y = y >> 1
        x = (x * x)
    return res""" 
"""def fact(n):
    if(n==0):
        return 1
    if(n==1):
        return 1
    return fact(n-1)+fact(n-2)"""

def maxPrimeFactors (n): 
    Prime = -1
    while n % 2 == 0: 
        Prime = 2
        n >>= 1  
    for i in range(3, int(math.sqrt(n)) + 1, 2): 
        while n % i == 0: 
            Prime = i 
            n = n / i 
    if n > 2: 
        Prime = n 
    return int(Prime)
#import collections
import math
array=[0]*100001
for i in range(1,100001):
    array[i]=maxPrimeFactors(i)
t=int(input())
for _ in range(t):
    n=int(input())
    #b,g=map(int,input().split())
    #x2,y2=map(int,input().split())
    arr=list(map(int,input().split()))
    #m,k=map(int,input().split())
    d={}
    for i in range(n):
        prime_fact=array[arr[i]]
        if prime_fact not in d:
            d[prime_fact]=1
        else:
            d[prime_fact]+=1
    maxCount=max(d.values())
    ans=-1
    for i in d:
        if(d[i]==maxCount):
            if(i>=ans):
              ans=i
    print(ans)
    


import math
def primes(n): 
    maxPrime = -1
      
    while n % 2 == 0: 
        maxPrime = 2
        n >>= 1 
    for i in range(3, int(math.sqrt(n)) + 1, 2): 
        while n % i == 0: 
            maxPrime = i 
            n = n / i 
    if n > 2: 
        maxPrime = n 
      
    return int(maxPrime) 

def prtable(n):
    dp=[0 for i in range(n+1)]
    dp[1]=1
    dp[2]=2
    dp[3]=3
    for i in range(4,n+1):
        dp[i]=primes(i)
    return dp
pr= prtable(100000)

for i in range(int(input())):
    n=int(input())
    a=list(map(int,input().split()))
    d={}
    for i in range(n):
        if pr[a[i]] in d:
            d[pr[a[i]]]+=1
        else:
            d[pr[a[i]]]=1
    ans=0
    maxx=0
    #print(d)

    for i in d:
        if d[i]>ans:
            ans=d[i]
            maxx=i
        elif d[i]==ans:
            if maxx<i:
                maxx=i
                ans=d[i]
    

    
            
    print(maxx)






















    

    


# cook your dish here
from collections import Counter


# Python3 program to find prime factorization 
# of a number n in O(Log n) time with 
# precomputation allowed. 
import math as mt 

MAXN = 100001

# stores smallest prime factor for 
# every number 
spf = [0 for i in range(MAXN)] 

# Calculating SPF (Smallest Prime Factor) 
# for every number till MAXN. 
# Time Complexity : O(nloglogn) 
def sieve(): 
    spf[1] = 1
    for i in range(2, MAXN): 
        
        # marking smallest prime factor 
        # for every number to be itself. 
        spf[i] = i 

    # separately marking spf for 
    # every even number as 2 
    for i in range(4, MAXN, 2): 
        spf[i] = 2

    for i in range(3, mt.ceil(mt.sqrt(MAXN))): 
        
        # checking if i is prime 
        if (spf[i] == i): 
            
            # marking SPF for all numbers 
            # divisible by i 
            for j in range(i * i, MAXN, i): 
                
                # marking spf[j] if it is 
                # not previously marked 
                if (spf[j] == j): 
                    spf[j] = i 

# A O(log n) function returning prime 
# factorization by dividing by smallest 
# prime factor at every step 
def getFactorization(x): 
    ret = list() 
    while (x != 1): 
        ret.append(spf[x]) 
        x = x // spf[x] 

    return ret.pop() #last ele 

# Driver code 

# precalculating Smallest Prime Factor 
sieve() 
# x = 12246

# calling getFactorization function 
# p = getFactorization(x) 

# for i in range(len(p)): 
#     print(p[i], end = " ") 

# This code is contributed 
# by Mohit kumar 29 


            
t = int(input())

for test in range(t):
    n = int(input())
    A = tuple(map(int, input().split()))
    li = []
    mx = 1
    mx_li = []
    for a in A:
        li.append(getFactorization(a))
      
    c = Counter(li)
    # print(li)
    # print(c)
    for key in c:
        if c[key] > mx:
            mx_li = [key]
            mx = c[key]
        elif c[key] == mx:
            mx_li.append(key)
    
    print(max(mx_li))
            


def prime(num):
  if n>1:
   for i in range(2, int(num**0.5)+1): 
         
       # If num is divisible by any number between  
       # 2 and n / 2, it is not prime  
       if (num % i) == 0: 
           return False
           break
   else: 
       return True
  
  else: 
   return False
t=int(input())
for k in range(t):
    n=int(input())
    a=[0]*n
    l=list(map(int,input().split()))
    s=max(l)
    a1=[0]*(s+1)
    i=2
    while(i<=s):
        if (prime(i)):
         for j in range(i,s+1,i):
            a1[j]=i
        i+=1
    for j in range(n):
        a[j]=a1[l[j]]
    a.sort()
    ti=1
    ma=1
    nu=a[0]
    for j in range(1,n):
        if a[j]==a[j-1]:
            ti+=1
        else:
            if ti>=ma:
                ma=ti
                nu=a[j-1]
                
            ti=1
    if ti>=ma:
        ma=ti
        nu=a[n-1]
        
    print(nu)
    
        


from collections import Counter
from math import sqrt

def facts(n):
    if n % 2 == 0:
        yield 2

        while n % 2 == 0:
            n //= 2

    for i in range(3, int(sqrt(n)) + 1, 2):
        if n % i == 0:
            yield i

            while n % i == 0:
                n //= i

    if n > 2:
        yield n

for _ in range(int(input())):
    n = int(input())
    a = list(map(int, input().split()))

    ms = [max(facts(i)) for i in a]

    cnt = Counter(ms)

    m = max(cnt.values())

    x = {i for i in ms if cnt[i] == m}

    print(max(x))