Mathematical knowledge: Nim game game theory

subject ：AcWing 891. Nim game
Given n Rubble , Two players take turns , Each operation can take any number of stones from any pile of stones （ You can finish it , But you have to take ）, In the end, those who can't do it are considered failures .

Ask if both of them adopt the optimal strategy , Whether the first is sure to win .

Input format
The first line contains integers n.

The second line contains n A digital , Among them the first i A number means the i The number of stones .

Output format
If you start first, you will win , The output Yes.

otherwise , Output No.

Data range
1≤n≤10⁵,
1≤ Number of stones per pile ≤10⁹

sample input ：

2
2 3

sample output ：

Yes

Topic analysis ：
This is the topic of game theory ,
Winning state ——> After the operation, the game can be in the state of first hand and failure
This problem uses XOR ,
a₁,a₂,a₃,…a_n Express n The number of stones
If a₁^a₂^a₃,…^a_n = 0 If you start, you'll lose
If a₁^a₂^a₃,…^a_n！=0 The first step is to win
If the XOR value is not 0, Then the XOR value must be 0
If the XOR value is 0, No matter how you take it, you won't let the XOR value be 0
because 0^0^0=0
So to sum up , Come to the conclusion

#include <iostream>
using namespace std;

const int N = 100010;

int main()
{
    
    int n,res=0;
    cin>>n;
    while(n--)
    {
    
        int x;
        cin>>x;
        res ^= x;
    }
    if(res)cout<<"Yes"<<endl;
    else cout<<"No"<<endl;
    return 0;
}