class Solution {
    Map<TreeNode, Integer> balance;
    int moves;

    public int distributeCoins(TreeNode root) {
        count(root);
        normalize(root);
        return moves;
    }

    private void normalize(TreeNode root) {
        if (root == null) return;

        normalize(root.left);
        normalize(root.right);
    }

    private void count(TreeNode root) {
        if (root == null) return;

        counts.put(root, root.val - 1 + count(root.left) + count(root.right));
    }
}