### Problem Statement :

Given a list of integers nums, return whether all numbers appear an even number of times.

This should be done in \mathcal{O}(1)O(1) space.

Constraints

n ≤ 100,000 where n is the length of nums

Example 1

Input

nums = [2, 4, 4, 2, 3, 3]

Output

True

Explanation

Every number occurs twice.

Example 2

Input

nums = [1]

Output

False

Explanation

1 occurs an odd number of times.

### Solution :

                        Solution in C++ :

bool solve(vector<int>& nums) {
int a = 0, b = 0;
for (auto x : nums) {
a ^= x;
b ^= x + 1;
}
return !a && !b;
}


                        Solution in Java :

import java.util.*;

class Solution {
public boolean solve(int[] nums) {
if (nums.length == 0 || nums.length % 2 == 1) {
return false;
}

Arrays.sort(nums);
for (int i = 0; i < nums.length; i += 2) {
if (nums[i] != nums[i + 1]) {
return false;
}
}
return true;
}
}


                        Solution in Python :

class Solution:
def solve(self, nums):
xor = 0
for x in nums:
# constants are primes arbitrarily taken from xxhash
hash = ((x + 0x9E3779B1) * 0x85EBCA77) & 0xFFFFFFFF
xor ^= hash
return xor == 0


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