class Solution:
def xor(self, arr):
if len(arr)%2==0:
print("YES")
return
else:
last = arr[0]
for i in range(1, len(arr), 1):
if last>= arr[i]:
print("YES")
return
else:
last = arr[i]
print("NO")
t = int(input())
obj = Solution()
for _ in range(t):
a = int(input())
arr = list(map(int, input().split()))
obj.xor(arr)
#include <iostream>
#include <bits/stdc++.h>
using namespace std;
long long int m;
void precalculate()
{
;
}
void testcase()
{
int n;
cin>>n;
int a[n];
for(int i=0;i<n;i++)
cin>>a[i];
if(n%2==0)
{
cout<<"YES"<<endl;
return;
}
for(int i=0;i<n-1;i++)
if(a[i]>=a[i+1])
{
cout<<"YES"<<endl;
return;
}
cout<<"NO"<<endl;
}
int main()
{
precalculate();
int t;
cin>>t;
while(t-->0)
testcase();
return 0;
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