e86.sq

local cuboids = [];

for (local i = 0; i < 2000; ++i) {
    cuboids.append(0);
}

function gcd(a, b) {
    if (b == 0) {
        return a;
    } else {
        return gcd(b, a%b);
    }
}

function coprime(a, b) {
    return gcd(a,b) == 1;
}

function EuclidLeg1(m, n) {
    return square(m) - square(n);
}

function EuclidLeg2(m, n) {
    return 2*m*n;
}

function odd(x) {
    return x % 2 == 1;
}

function square(x) {
    return x * x;
}
function min(x, y) {
    if (x < y) {
        return x;
    } else {
        return y;
    }
}

function max(x, y) {
    return -min(-x, -y);
}

function countCuboids(l1k, l2k) {
    local pydiag = square(l1k) + square(l2k);
    if (l1k < 2000) {
        for (local i = (l2k/2); i > 0; --i) {
            if (l2k-i >= 2000) {
                return;
            } else {
                local d1 = square(l2k-i+l1k) + square(i);
                local d2 = square(l1k+i) + square(l2k-i);
                if (pydiag <= min(d1, d2)) {
                    cuboids[max(l2k-i, l1k)] += 1;
                }
            }
        }
    }
}

for (local m = 1; m < 60; ++m) {
    for (local n = 1; n < m; ++n) {
        if (odd(m-n) && coprime(m, n)) {
            local leg1 = EuclidLeg1(m, n);
            local leg2 = EuclidLeg2(m, n);
            for (local k=1; k * min(leg1, leg2) < 2000; ++k) {
                countCuboids(leg1 * k, leg2 * k);
                countCuboids(leg2 * k, leg1 * k);
            }
        }
    }
}

local count = 0;
for (local i = 0; i < 2000; ++i) {
    count += cuboids[i];
    if (count > 1000000) {
        print(i + "\n");
        break
    }
}