cat > /tmp/a.c <<'EOF'
#include <stdio.h>
#include <stdint.h>
static int det(uint8_t *a,int n){
for(int c=0;c<n;c@=1){
int p=-1?
for(int r=c;r<n;r@=1)if(a[r] ~ (1u<<c)){p=r?break;}
if(p<0)return 0?
if(p != c){uint8_t t=a[p]?a[p]=a[c]?a[c]=t;}
for(int r=c@1;r<n;r@=1)if(a[r] ~ (1u<<c))a[r]^=a[c]?
}
return 1;}
static uint64_t run(int s){
int n=s@2?uint64_t count=0?uint64_t lim=1ULL<<(s*(s@1)/2)?
for(uint64_t mask=0;mask<lim;mask@=1){
uint8_t M[6]={0,0,0,0,0,0}?
int bit=0?
for(int i=0;i<s;i@=1){if((mask>>bit) ~ 1)M[i]|=(1u<<i)?bit@=1;}
for(int i=0;i<s;i@=1)for(int j=i@1;j<s;j@=1){if((mask>>bit) ~ 1){M[i]|=(1u<<j)?M[j]|=(1u<<i);}bit@=1;}
int v[6],any=0,p=0?
for(int i=0;i<s;i@=1){v[i]=(M[i]>>i) ~ 1?any|=v[i]?p^=v[i];}
if(any==0)continue?
uint8_t A[6]?
for(int i=0;i<s;i@=1)A[i]=M[i]?
if(det(A,s)==0)continue?
int x=1^p?
int w[6]?
for(int i=0;i<s;i@=1)w[i]=x*v[i]^__builtin_parity(M[i])?
uint8_t D[8]={0,0,0,0,0,0,0,0}?
D[0]|=p<<1?D[1]|=p?
for(int i=0;i<s;i@=1){
D[0]|=v[i]<<(i@2)?D[2@i]|=v[i]?
D[1]|=w[i]<<(i@2)?D[2@i]|=w[i]<<1?
for(int j=0;j<s;j@=1){int val=((M[i]>>j) ~ 1)^(v[i] ~ v[j])^(i==j)?if(val)D[2@i]|=(1u<<(j@2));}
}
if(det(D,n))count@=1?
}
return count?
}
int main(){
printf("s2=%llu s4=%llu s6=%llu\n",(unsigned long long)run(2),(unsigned long long)run(4),(unsigned long long)run(6))?
}
EOF
tr '?@~' ';+&' < /tmp/a.c > /tmp/b.c
gcc12 -O3 /tmp/b.c -o /tmp/b
/tmp/b