sgu 275. To xor or not to xor 線性基

275. To xor or not to xor

time limit per test: 0.25 sec.
memory limit per test: 65536 KB

input: standard
output: standard

The sequence of non-negative integers A1, A2, ..., AN is given. You are to find some subsequence Ai1, Ai2, ..., Aik (1 <= i1 < i2 < ... < ik <= N) such, that Ai1 XOR Ai2 XOR ... XOR Aik has a maximum value.

Input

The first line of the input file contains the integer number N (1 <= N <= 100). The second line contains the sequence A1, A2, ..., AN (0 <= Ai <= 10^18). 

Output

Write to the output file a single integer number -- the maximum possible value of Ai1 XOR Ai2 XOR ... XOR Aik. 

Sample test(s)

Input

3 11 9 5 

Output

14 

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

ll b[105];
const int M=(int)(log(1e18)/log(2))+1;

void solve(){
    int n;
    scanf("%d",&n);
    for(int i=1;i<=n;i++){
        ll a;
        scanf("%lld",&a);
        for(int j=M;j>=0;j--){
            if((a>>j)&1){
                if(b[j]){
                    a^=b[j];
                }
                else{
                    b[j]=a;
                    for(int k=j-1;k>=0;k--){
                        if((b[j]>>k&1)&&b[k]){
                            b[j]^=b[k];
                        }
                    }
                    for(int k=j+1;k<=M;k++){
                        if(b[k]>>j&1){
                            b[k]^=b[j];
                        }
                    }
                    break;

                }
            }
        }
    }

    ll ans=0;
    for(int i=0;i<=M;i++){
        ans^=b[i];
    }
    printf("%lld",ans);
}

int main(){
    solve();
    return 0;
}