#!/bin/sh
cat >/tmp/a.c <<E
#include <stdio.h>
typedef unsigned short u;int rk(u*m,int n){int r=0;for(int c=0;c<n;c++){u b=1<<c;int p=-1;for(int i=r;i<n;i++)if(m[i]&b){p=i;break;}if(p<0)continue;u t=m[r];m[r]=m[p];m[p]=t;u x=m[r];for(int i=r+1;i<n;i++)if(m[i]&b)m[i]^=x;r++;}return r;}void inv(u*m,u*f,int n){u a[8];for(int i=0;i<n;i++)a[i]=m[i]|(1<<(n+i));for(int c=0;c<n;c++){u b=1<<c;int p=-1;for(int i=c;i<n;i++)if(a[i]&b){p=i;break;}if(p<0)return;u t=a[c];a[c]=a[p];a[p]=t;u x=a[c];for(int i=0;i<n;i++)if(i!=c&&(a[i]&b))a[i]^=x;}for(int i=0;i<n;i++)f[i]=a[i]>>n;}int main(){int ts[2]={4,6};for(int z=0;z<2;z++){int t=ts[z],n=t+2;long cnt=0;int e=t*(t-1)/2;u W[8],F[8],A[8],B[8];for(int mask=0;mask<(1<<e);mask++){for(int i=0;i<t;i++)W[i]=0;int k=0;for(int i=0;i<t;i++)for(int j=i+1;j<t;j++){if((mask>>k)&1){W[i]|=1<<j;W[j]|=1<<i;}k++;}for(int i=0;i<t;i++)B[i]=W[i];if(rk(B,t)<t)continue;inv(W,F,t);int full=(1<<t)-1;for(int lm=0;lm<=full;lm++){if(lm==0||lm==full)continue;A[0]=lm<<2;A[1]=(full^lm)<<2;for(int i=0;i<t;i++){u d=0;for(int j=0;j<t;j++)if(((lm>>i)&1)==((lm>>j)&1))d|=1<<j;A[2+i]=(((lm>>i)&1)?1:2)|((F[i]^d)<<2)^(1<<(2+i));}for(int i=0;i<n;i++)B[i]=A[i];if(rk(B,n)==n)cnt++;}}printf("%d %ld\n",t,cnt);}return 0;}
E
cc -w -O2 -o /tmp/a /tmp/a.c && /tmp/a