// The Great Computer Language Shootout

// http://shootout.alioth.debian.org/

//

// contributed by Ian Osgood

function A(i,j) {

  return 1/((i+j)*(i+j+1)/2+i+1);

}

function Au(u,v) {

  for (var i=0; i<u.length; ++i) {

    var t = 0;

    for (var j=0; j<u.length; ++j)

      t += A(i,j) * u[j];

    v[i] = t;

  }

}

function Atu(u,v) {

  for (var i=0; i<u.length; ++i) {

    var t = 0;

    for (var j=0; j<u.length; ++j)

      t += A(j,i) * u[j];

    v[i] = t;

  }

}

function AtAu(u,v,w) {

  Au(u,w);

  Atu(w,v);

}

function spectralnorm(n) {

  var i, u=[], v=[], w=[], vv=0, vBv=0;

  for (i=0; i<n; ++i) {

    u[i] = 1; v[i] = w[i] = 0;

  }

  for (i=0; i<10; ++i) {

    AtAu(u,v,w);

    AtAu(v,u,w);

  }

  for (i=0; i<n; ++i) {

    vBv += u[i]*v[i];

    vv  += v[i]*v[i];

  }

  return Math.sqrt(vBv/vv);

}

for (var i = 6; i <= 48; i *= 2) {

    spectralnorm(i);

}