// Synthetic specification counterexample only; not a production selector.
import assert from 'node:assert/strict';
const cases=[{id:'middle',start:1,end:3,stratum:'S'},{id:'left',start:0,end:2,stratum:'S'},{id:'right',start:2,end:4,stratum:'N'}];
const valid=a=>a.filter(x=>x.stratum==='S').length<=1&&a.filter(x=>x.stratum==='N').length<=1&&a.every((x,i)=>a.slice(i+1).every(y=>Math.max(x.start,y.start)>=Math.min(x.end,y.end)));
let greedy=[];for(const x of cases)if(valid([...greedy,x]))greedy.push(x);
let best=[];for(let mask=0;mask<8;mask++){const a=cases.filter((_,i)=>mask&(1<<i));if(valid(a)&&a.length>best.length)best=a;}
assert.equal(greedy.length,1);assert.equal(best.length,2);
console.log(JSON.stringify({synthetic:true,greedy:greedy.map(x=>x.id),maximum_feasible:best.map(x=>x.id),production_verified:false}));