CF1594E1.Rubik's Cube Coloring (easy version)

It is the easy version of the problem. The difference is that in this version, there are no nodes with already chosen colors.

Theofanis is starving, and he wants to eat his favorite food, sheftalia. However, he should first finish his homework. Can you help him with this problem?

You have a perfect binary tree of $2^k - 1$ nodes — a binary tree where all vertices $i$ from $1$ to $2^{k - 1} - 1$ have exactly two children: vertices $2i$ and $2i + 1$. Vertices from $2^{k - 1}$ to $2^k - 1$ don't have any children. You want to color its vertices with the $6$ Rubik's cube colors (White, Green, Red, Blue, Orange and Yellow).

Let's call a coloring good when all edges connect nodes with colors that are neighboring sides in the Rubik's cube.

A picture of Rubik's cube and its 2D map.

More formally:

• a white node can not be neighboring with white and yellow nodes;
• a yellow node can not be neighboring with white and yellow nodes;
• a green node can not be neighboring with green and blue nodes;
• a blue node can not be neighboring with green and blue nodes;
• a red node can not be neighboring with red and orange nodes;
• an orange node can not be neighboring with red and orange nodes;

You want to calculate the number of the good colorings of the binary tree. Two colorings are considered different if at least one node is colored with a different color.

The answer may be too large, so output the answer modulo $10^9+7$.

这是该问题的简单版本。区别在于，在此版本中，没有任何节点已被预先指定颜色。

西奥法尼斯饿了，他想吃自己最爱的食物——希夫塔利亚香肠。但在此之前，他必须先完成作业。你能帮他解决这个问题吗？

你有一棵包含 $2^k - 1$ 个节点的完美二叉树——即：对所有从 $1$ 到 $2^{k - 1} - 1$ 的顶点 $i$，其恰好有两个子节点：顶点 $2i$ 和 $2i + 1$；而从 $2^{k - 1}$ 到 $2^k - 1$ 的顶点则没有子节点。你需要用魔方的六种颜色（白色、绿色、红色、蓝色、橙色和黄色）为这棵树的所有顶点染色。

若一棵树的所有边所连接的两个顶点的颜色，在魔方中对应相邻面，则称该染色方案为合法染色。

魔方实物图及其二维展开图。

更形式化地，禁止的相邻关系如下：

• 白色顶点不能与白色或黄色顶点相邻；
• 黄色顶点不能与白色或黄色顶点相邻；
• 绿色顶点不能与绿色或蓝色顶点相邻；
• 蓝色顶点不能与绿色或蓝色顶点相邻；
• 红色顶点不能与红色或橙色顶点相邻；
• 橙色顶点不能与红色或橙色顶点相邻；

你需要计算该二叉树的合法染色方案总数。若至少有一个顶点的颜色不同，则认为两种染色方案不同。

答案可能非常大，请输出其对 $10^9+7$ 取模的结果。

The first and only line contains the integers $k$ ($1 \le k \le 60$) — the number of levels in the perfect binary tree you need to color.

第一行且唯一一行包含一个整数 $k$（$1 \le k \le 60$）——即你需要染色的完美二叉树的层数。

Print one integer — the number of the different colorings modulo $10^9+7$.

输出一个整数——不同染色方案的数量对 $10^9+7$ 取模的结果。

In the picture below, you can see one of the correct colorings of the first example.

在下面的图片中，您可以看到第一个示例的一个正确染色方案。