Mathematical knowledge: step Nim game game game theory

subject ：AcWing 892. steps -Nim game
Now? , There is one n Stairs of steps , There are several stones on each step , Among them the first i There are... On the steps a_i A stone (i≥1).

Two players take turns , Each operation can take several stones from any step and put them into the next step （ You can't stop taking ）.

You can't take the stones on the ground anymore , 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 It's an integer , Among them the first i An integer represents the th i Number of stones on steps a_i.

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

otherwise , Output No.

Data range
1≤n≤10⁵,
1≤a_i≤10⁹

sample input ：

3
2 1 3

sample output ：

Yes

Topic analysis ：
This question is similar to the previous one
a₁^a₃^a₅…^a_n!=0 If you start, you will win
The strategy of winning first ：
If you take even steps , Then put it on the next step , Will keep the odd steps unchanged .
If you take odd steps , Then XOR is not 0, Then the operation makes its XOR become 0.
conversely , If XOR is 0, Then the backhand wins .

#include <iostream>

using namespace std;

int main()
{
    
    int n;
    cin>>n;
    int res=0;
    for(int i=1;i<=n;i++)
    {
    
        int x;
        cin>>x;
        if(i%2)res^=x;
    }
    if(res)cout<<"Yes"<<endl;
    else cout<<"No"<<endl;
    return 0;
}