CF1205C.Palindromic Paths

This is an interactive problem

You are given a grid $n\times n$, where $n$ is odd. Rows are enumerated from $1$ to $n$ from up to down, columns are enumerated from $1$ to $n$ from left to right. Cell, standing on the intersection of row $x$ and column $y$, is denoted by $(x, y)$.

Every cell contains $0$ or $1$. It is known that the top-left cell contains $1$, and the bottom-right cell contains $0$.

We want to know numbers in all cells of the grid. To do so we can ask the following questions:

"$?$ $x_1$ $y_1$ $x_2$ $y_2$", where $1 \le x_1 \le x_2 \le n$, $1 \le y_1 \le y_2 \le n$, and $x_1 + y_1 + 2 \le x_2 + y_2$. In other words, we output two different cells $(x_1, y_1)$, $(x_2, y_2)$ of the grid such that we can get from the first to the second by moving only to the right and down, and they aren't adjacent.

As a response to such question you will be told if there exists a path between $(x_1, y_1)$ and $(x_2, y_2)$, going only to the right or down, numbers in cells of which form a palindrome.

For example, paths, shown in green, are palindromic, so answer for "$?$ $1$ $1$ $2$ $3$" and "$?$ $1$ $2$ $3$ $3$" would be that there exists such path. However, there is no palindromic path between $(1, 1)$ and $(3, 1)$.

Determine all cells of the grid by asking not more than $n^2$ questions. It can be shown that the answer always exists.

这是一个交互式问题。

给定一个 $n\times n$ 的网格，其中 $n$ 为奇数。行从上到下编号为 $1$ 到 $n$，列从左到右编号为 $1$ 到 $n$。位于第 $x$ 行、第 $y$ 列的格子记作 $(x, y)$。

每个格子中包含数字 $0$ 或 $1$。已知左上角格子 $(1,1)$ 中为 $1$，右下角格子 $(n,n)$ 中为 $0$。

我们的目标是确定网格中所有格子内的数字。为此，你可以提出如下形式的问题：

“$?$ $x_1$ $y_1$ $x_2$ $y_2$”，其中 $1 \le x_1 \le x_2 \le n$，$1 \le y_1 \le y_2 \le n$，且满足 $x_1 + y_1 + 2 \le x_2 + y_2$。换言之，你输出网格中两个不同的格子 $(x_1, y_1)$ 和 $(x_2, y_2)$，使得仅通过向右或向下移动即可从第一个格子到达第二个格子，且这两个格子不相邻。

对于该问题，系统将返回：是否存在一条仅向右或向下移动、连接 $(x_1, y_1)$ 与 $(x_2, y_2)$ 的路径，使得该路径上所有格子中的数字构成一个回文串。

例如，图中以绿色标出的路径均为回文路径，因此对问题 “$?$ $1$ $1$ $2$ $3$” 和 “$?$ $1$ $2$ $3$ $3$” 的回答均为“存在这样的路径”。然而，在 $(1,1)$ 与 $(3,1)$ 之间并不存在回文路径。

请通过不超过 $n^2$ 次提问，确定网格中所有格子的数值。可以证明答案恒存在。

The first line contains odd integer ($3 \le n \lt 50$) — the side of the grid.

第一行包含一个奇数整数（$3 \le n \lt 50$）——网格的边长。