平衡树 - Problem

#10836. 平衡树

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AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

如果一棵二叉树 $T$ 为空，或者同时满足以下三个条件，则称其为超平衡（super balanced）二叉树：

$T$ 的左子树是超平衡的。
$T$ 的右子树是超平衡的。
$T$ 的左子树节点数与右子树节点数之差不超过 1。

请计算由 $n$ 个节点组成的超平衡二叉树的数量。由于答案可能非常大，请输出答案对 $2^{64}$ 取模的结果。

输入格式

第一行包含一个整数 $T$ ($1 \le T \le 10^6$)，表示测试用例的数量。每个测试用例包含一个整数 $n$ ($0 \le n < 2^{64}$)，表示树中的节点数。

输出格式

对于每个测试用例，输出一行，包含一个整数，表示由 $n$ 个节点组成的超平衡二叉树的数量。

样例

样例输入 1

2
2
3

样例输出 1

2
1

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