# This Algae routine counts the number of "Euler constellations"
# in the first `n' positive integers.  An "Euler constellation"
# is an irredundant set of positive integers `a' through `h'
# such that the sum of `a', `b', `c', and `d', the sum of the
# squares of `a', `b', `c', and `d', and the sum of the cubes
# of `a', `b', `c', and `d' are equal to the corresponding
# sums for `e', `f', `g', and `h'.

n = 16;

check = function( a; b; c; d; e; f; g; h ) {
    if ( a+b+c+d == e+f+g+h ) {
        if ( a^2+b^2+c^2+d^2 == e^2+f^2+g^2+h^2 ) {
            if ( a^3+b^3+c^3+d^3 == e^3+f^3+g^3+h^3 ) {
                return 1;
            }
        }
    }
    return 0;
};

cnt = 0;

for ( a in 8:n ) {
  for ( b in 7:a-1 ) {
    for ( c in 6:b-1 ) {
      for ( d in 5:c-1 ) {
        for ( e in 4:d-1 ) {
          for ( f in 3:e-1 ) {
            for ( g in 2:f-1 ) {
              for ( h in 1:g-1 ) {

                if ( check( a; b; c; d;  e; f; g; h ) ) { cnt += 1; continue; }
                if ( check( a; e; c; d;  b; f; g; h ) ) { cnt += 1; continue; }
                if ( check( a; f; c; d;  e; b; g; h ) ) { cnt += 1; continue; }
                if ( check( a; g; c; d;  e; f; b; h ) ) { cnt += 1; continue; }
                if ( check( a; h; c; d;  e; f; g; b ) ) { cnt += 1; continue; }
                if ( check( a; b; e; d;  c; f; g; h ) ) { cnt += 1; continue; }
                if ( check( a; b; f; d;  e; c; g; h ) ) { cnt += 1; continue; }
                if ( check( a; b; g; d;  e; f; c; h ) ) { cnt += 1; continue; }
                if ( check( a; b; h; d;  e; f; g; c ) ) { cnt += 1; continue; }
                if ( check( a; b; c; e;  d; f; g; h ) ) { cnt += 1; continue; }
                if ( check( a; b; c; f;  e; d; g; h ) ) { cnt += 1; continue; }
                if ( check( a; b; c; g;  e; f; d; h ) ) { cnt += 1; continue; }
                if ( check( a; b; c; h;  e; f; g; d ) ) { cnt += 1; continue; }
                if ( check( a; e; f; d;  b; c; g; h ) ) { cnt += 1; continue; }
                if ( check( a; e; g; d;  b; f; c; h ) ) { cnt += 1; continue; }
                if ( check( a; e; h; d;  b; f; g; c ) ) { cnt += 1; continue; }
                if ( check( a; f; g; d;  e; b; c; h ) ) { cnt += 1; continue; }
                if ( check( a; f; h; d;  e; b; g; c ) ) { cnt += 1; continue; }
                if ( check( a; g; h; d;  e; f; b; c ) ) { cnt += 1; continue; }
                if ( check( a; b; e; f;  c; d; g; h ) ) { cnt += 1; continue; }
                if ( check( a; b; e; g;  c; f; d; h ) ) { cnt += 1; continue; }
                if ( check( a; b; e; h;  c; f; g; d ) ) { cnt += 1; continue; }
                if ( check( a; b; f; g;  e; c; d; h ) ) { cnt += 1; continue; }
                if ( check( a; b; f; h;  e; c; g; d ) ) { cnt += 1; continue; }
                if ( check( a; b; g; h;  e; f; c; d ) ) { cnt += 1; continue; }
                if ( check( a; e; f; g;  e; f; g; h ) ) { cnt += 1; continue; }
                if ( check( a; e; f; h;  e; f; g; h ) ) { cnt += 1; continue; }
                if ( check( a; e; g; h;  e; f; g; h ) ) { cnt += 1; continue; }
                if ( check( a; f; g; h;  e; f; g; h ) ) { cnt += 1; continue; }

              }
            }
          }
        }
      }
    }
  }
}