Chef got into a fight with the evil Dr Doof. Dr Doof has decided to destroy all even numbers from the universe using his Evil-Destroy-inator. Chef has $N$ integers with him. To stop Doof, Chef has to find an odd number which is an integer multiple of all $N$ numbers that he has with him. Find if it is possible for Chef to prevent Dr Doof from destroying the even numbers.
Formally, given $N$ positive integers, find if there exists an odd number which is an integer multiple of all the given $N$ numbers. If yes, print "YES", otherwise "NO". You can print any letter in any case.

-----Input-----
- First line contains $T$, number of testcases. Each testcase consists of $2$ lines.
- The first line of each test case consists of a positive integer $N$, denoting the number of positive integers Chef has.
- The second line of each test case contains $N$ space separated integers $A_i$ each denoting an integer that Chef has with him.

-----Output-----
For every test case, if there exists such an odd number, print "YES" on a separate line, otherwise "NO". The judge is case insensitive. That means, your code can print any letter in any case ( "Yes", "yes" or "YES" are all accepted).

-----Constraints-----
- $1 \leq T \leq 10^3$
- $1 \leq N \leq 10^3$
- $1 \leq A_i \leq 10^3$

-----Sample Input-----
2
5
1 2 5 4 3
1
7

-----Sample Output-----
NO
YES

-----Explanation-----
For test $1$: There exists no odd number.
For test $2$: The possible odd numbers can be $7$, $21$, $49$, $315$, …

Difficulty: interview

Starter code:

Solutions:
def gcd(a,b):
 if b==0: return a
 return gcd(b,a%b)

for _ in range(int(input())):
 n = int(input())
 arr = list(map(int,input().split()))
 value = arr[0]
 if n!=1:
  for i in arr[1:]:
   value = value*i//gcd(value, i)
 if value%2==0:
  print("NO")
 else:
  print("YES")

# cook your dish here
t=int(input())
for i in range(t):
 n=int(input())
 q=list(map(int,input().split()))
 p=0
 for j in q:
  if j%2!=0:
   p+=1
 if p==len(q):
  print("YES")
 else:
  print("NO")
  


for _ in range(int(input())):
 N=int(input())
 A=list(map(int,input().strip().split()))
 c=0
 for i in range(N):
  if A[i] & 1:
   continue
  else:
   c=1
   break
 if c==0:
  print("YES")
 else:
  print("NO")

# cook your dish here
for t in range(int(input())):
 n=int(input())
 arr=list(map(int,input().split()[:n]))
 c=1
 for i in arr:
  c=c*i
 if c%2!=0:
  print("YES")
 else:
  print("NO")

# cook your dish here
for _ in range(0,int(input())):
 n=int(input())
 l=list(map(int,input().split()))
 cnt=0
 for i in range(0,n):
  if(l[i]%2==0):
   cnt+=1 
   print("NO")
   break
 if(cnt==0):
  print("YES")


# cook your dish here
import numpy
for _ in range( int (input())):
 n= int(input())
 a = list( map ( int, input().split() ) )
 s = numpy.prod(a) 
 if s % 2 == 0:
  print('NO')
 else:
  print('YES')

t=int(input())
for _ in range(t):
 n=int(input())
 l=list(map(int,input().split()))
 flag=True
 for i in l:
  if i%2==0:
   flag=False
   break
 if flag:
  print("YES")
 else:
  print("NO")

# cook your dish here
import numpy
for _ in range( int (input())):
 n= int(input())
 a = list( map ( int, input().split() ) )
 s = numpy.prod(a) 
 if s % 2 == 0:
  print('NO')
 else:
  print('YES')

import math
def gcd(a,b): 
 if (b == 0): 
   return a 
 return gcd(b, a%b) 

def lcm(a,b): 
 return (a*b) / gcd(a,b) 

def bs(arr, l, r, x): 
 while l <= r: 
  mid = l + (r - l)//2; 
  if(arr[mid]==x): 
   return arr[mid]
  elif(arr[mid]<x): 
   l = mid + 1
  else: 
   r = mid - 1
 return -1

def swap(list, pos1, pos2): 
  
 list[pos1], list[pos2] = list[pos2], list[pos1] 
 return list

t = int(input())
for _ in range(t):
 n = int(input())
 a = list(map(int,input().split()))
 f = 0
 for i in range(n):
  if(a[i]%2==0):
   f=1
 if(f):
  print('NO')
 else:
  print('YES')

#chef and droof
for u in range(int(input())):
 flag = 0
 n = int(input())
 lst = list(map(int,input().split()))
 for i in range(n):
  if lst[i] % 2 ==0:
   flag = 1
   break
 if flag == 0:
  print("YES")
 else:
  print("NO")


# cook your dish here
# cook your dish here
try:
 t = int(input())
 for _ in range(t):
  n = int(input())
  p = 1
  a = [int(x) for x in input().split()]
  for item in a:
   p = p*item
  if p%2==0:
   print("NO")
  else:
   print("YES")

except:
 pass

# cook your dish here
test = int(input())

for _ in range(test):
 
 flag = 0
 N = int(input())
 arr = list(map(int,input().split()))
 
 for i in arr:
  if i%2 == 0:
   print("NO")
   flag = 1
   break
 
 if flag == 0:
  print("YES")

# cook your dish here
t=int(input())
for l in range(t):
 n=int(input())
 t=list(map(int,input().strip().split()))
 for i in t:
  if i%2==0:
   print("NO")
   break
 else:
  print("YES")

# cook your dish here

def find_lcm(num1, num2):
 if (num1 > num2):
  num = num1
  den = num2
 else:
  num = num2
  den = num1
 rem = num % den
 while (rem != 0):
  num = den
  den = rem
  rem = num % den
 gcd = den
 lcm = (int(num1 * num2) // int(gcd))
 return lcm
t=int(input())
for num in range(t):
 n=int(input())
 l = list(map(int, input().split()))
 if len(l)==1:
  if l[0]%2==0:
   print("NO")
  else:
   print("YES")

 else:
  num1 = l[0]
  num2 = l[1]
  lcm = find_lcm(num1, num2)

  for i in range(2, len(l)):
   lcm = find_lcm(lcm, l[i])

  if lcm % 2 == 0:
   print("NO")
  else:
   print("YES")










# cook your dish here


for testcase in range(int(input())):
 n=int(input())
 sol=[int(i) for i in input().split()]
 main=1
 a=[0]*10
 for z in sol:
  if(z%2==0):
   main=0
 if(main):
  print("YES")
 else:
  print("NO")

for _ in range(int(input())):
 n = int(input())
 l = list(map(int, input().split()))
 
 flag = 0
 for i in l:
  if i % 2 == 0:
   flag = 1
   break
 
 if flag:
  print("NO")
 else:
  print("YES")

# cook your dish here
t=int(input())
for t1 in range(t):
 n=int(input())
 l=[int(x) for x in input().split()]
 prod=1
 for i in l:
  prod=prod*i
 if(prod%2==1):
  print('YES')
 else:
  print('NO')

# cook your dish here
t = int(input())
while t:
 t -= 1
 n = int(input())
 ls = list(map(int,input().split()))
 flag=1
 for item in ls:
  if item%2==0:
   flag=0
   break
 if flag==0:
  print("NO")
 else:
  print("YES")

for i in range (int(input())) :
 a = int(input())
 b = list(map(int, input().split()))
 flag = 0
 for j in b :
  if j % 2 == 0 :
   flag += 1
   break
 if flag == 0 :
  print("YES")
 else :
  print("NO")

# cook your dish here
import numpy
for _ in range( int (input())):
 n= int(input())
 a = list( map ( int, input().split() ) )
 s = numpy.prod(a) 
 if s % 2 == 0:
  print('NO')
 else:
  print('YES')