let N: int = 8;
        
namespace Global(N); 
    let alpha: expr = std::prelude::challenge(0, 41);
    let beta: expr = std::prelude::challenge(0, 42);
    col fixed INCREMENTAL(i) {i+1};
    col witness x;
    col witness stage(1) y;
    x = INCREMENTAL;
    y = x + beta * alpha;

    public out = y(N - 1);
    public out_sec= x(N - 1);