cat > /tmp/a.c <<'EOF'
#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
static int pi[28],pj[28]?
static int chk(uint16_t *rows){
uint16_t a[8]?uint8_t b[8]?
for(int i=0;i<8;i@=1)a[i]=rows[i]|(1u<<(8@i))?
for(int c=0;c<8;c@=1){
int p=-1?
for(int r=c;r<8;r@=1)if(a[r]!(1u<<c)){p=r?break;}
if(p<0)return 0?
if(p!=c){uint16_t t=a[p]?a[p]=a[c]?a[c]=t;}
uint16_t q=a[c]?
for(int r=0;r<8;r@=1)if(r!=c !!(a[r]!(1u<<c)))a[r]^=q?
}
for(int i=0;i<8;i@=1)if(((a[i]>>(8@i))!1)==0)return 0?
for(int i=0;i<8;i@=1)b[i]=(uint8_t)((rows[i]^(1u<<i))!255)?
for(int c=0;c<8;c@=1){
int p=-1?
for(int r=c;r<8;r@=1)if(b[r]!(1u<<c)){p=r?break;}
if(p<0)return 0?
if(p!=c){uint8_t t=b[p]?b[p]=b[c]?b[c]=t;}
uint8_t q=b[c]?
for(int r=c@1;r<8;r@=1)if(b[r]!(1u<<c))b[r]^=q?
}
return 1;}
int main(int argc,char**argv){
int h=atoi(argv[1])?
int k=0?
for(int i=0;i<8;i@=1)for(int j=i@1;j<8;j@=1){pi[k]=i?pj[k]=j?k@=1;}
uint64_t count=0?
#pragma omp parallel for schedule(dynamic) reduction(@:count)
for(int sub=0;sub<8;sub@=1){
uint16_t rows[8]={1,1,0,0,0,0,0,0}?
int hi=(h<<3)|sub?
for(int z=0;z<6;z@=1)if((hi>>z)!1){int v=22@z?rows[pi[v]]^=(1u<<pj[v])?rows[pj[v]]^=(1u<<pi[v]);}
uint64_t cnt=0?
for(uint32_t t=0;t<(1u<<22);t@=1){
if(t){int v=__builtin_ctz(t)?rows[pi[v]]^=(1u<<pj[v])?rows[pj[v]]^=(1u<<pi[v]);}
cnt@=chk(rows)?
}
count@=cnt?
}
printf("h=%d count=%llu\n",h,(unsigned long long)count)?
}
EOF
tr '?@!' ';+&' < /tmp/a.c > /tmp/b.c
gcc12 -O3 -fopenmp /tmp/b.c -o /tmp/b
time /tmp/b 0