function addChild(tree, c, node, child) {
    tree[node] = tree[node] ?? { children: new Set(), val: c[node - 1] };
    tree[node].children.add(child);
}

function cleanUpTree(tree, node = 1, parent = -1, vMap = {}) {
    let { children, val } = tree[node];
    children.delete(parent);
    for (const child of children) {
        const [v] = cleanUpTree(tree, child, node, vMap);
        val += v;
    }
    vMap[val] = (vMap[val] ?? 0) + 1;
    tree[node].val = val;
    return [val, vMap];
}

function getMin(a, b) {
    return a === -1 || a > b ? b : a;
}

function* dfsIter(tree, vMap, node = 1, parentVMap = {}) {
    const { val, children } = tree[node];
    vMap[val]--;
    parentVMap[val] = (parentVMap[val] ?? 0) + 1;
    for (const child of children)
        yield* dfsIter(tree, vMap, child, parentVMap);
    parentVMap[val]--;
    if (node === 1) return;
    yield [val, parentVMap];
}

function balancedForest(c, edges) {
    let ret = -1;
    if (!c?.length || !edges?.length) return ret;

    const tree = {};
    for (const [begin, end] of edges) {
        addChild(tree, c, begin, end);
        addChild(tree, c, end, begin);
    }
    const [total, vMap] = cleanUpTree(tree);

    for (const [v1, parentVMap] of dfsIter(tree, vMap)) {
        const rest = total - v1;

        if (rest === v1) {
            ret = getMin(ret, v1);
            continue;
        }

        for (const v2 of [rest / 2, v1, rest - v1]) {
            if (!vMap[v2] && !parentVMap[v1 + v2]) continue;
            const v3 = rest - v2;

            const [a, b, c] = [v1, v2, v3].sort((a, b) => b - a);
            if (a !== b) continue;

            ret = getMin(ret, a - c);
        }
    }
    return ret;
}