CF1291A.Even But Not Even

Let's define a number ebne (even but not even) if and only if its sum of digits is divisible by $2$ but the number itself is not divisible by $2$. For example, $13$, $1227$, $185217$ are ebne numbers, while $12$, $2$, $177013$, $265918$ are not. If you're still unsure what ebne numbers are, you can look at the sample notes for more clarification.

You are given a non-negative integer $s$, consisting of $n$ digits. You can delete some digits (they are not necessary consecutive/successive) to make the given number ebne. You cannot change the order of the digits, that is, after deleting the digits the remaining digits collapse. The resulting number shouldn't contain leading zeros. You can delete any number of digits between $0$ (do not delete any digits at all) and $n-1$.

For example, if you are given $s=$222373204424185217171912 then one of possible ways to make it ebne is: 222373204424185217171912 $\rightarrow$ 2237344218521717191. The sum of digits of 2237344218521717191 is equal to $70$ and is divisible by $2$, but number itself is not divisible by $2$: it means that the resulting number is ebne.

Find any resulting number that is ebne. If it's impossible to create an ebne number from the given number report about it.

我们定义一个数为 ebne 数（偶但不偶），当且仅当它的各位数字之和能被 $2$ 整除，但该数本身不能被 $2$ 整除。例如，$13$、$1227$、$185217$ 是 ebne 数，而 $12$、$2$、$177013$、$265918$ 不是。如果你仍不确定 ebne 数的定义，可以参考样例说明以获得进一步澄清。

给你一个由 $n$ 位数字组成的非负整数 $s$。你可以删除其中一些数字（这些数字不必连续），使得剩余数字构成的数为 ebne 数。你不能改变剩余数字的顺序，即删除后剩余数字会自动“坍缩”成一个新数。结果数不得包含前导零。你可以删除 $0$（即不删任何数字）至 $n-1$ 个数字之间的任意数量的数字。

例如，若给定 $s = $222373204424185217171912，则一种可能的构造 ebne 数的方式是：
222373204424185217171912 $\rightarrow$ 2237344218521717191。
该结果数 $2237344218521717191$ 的各位数字之和为 $70$，可被 $2$ 整除；但该数本身是奇数（不能被 $2$ 整除），因此它是一个 ebne 数。

请找出任意一个满足条件的 ebne 数。如果无法从给定数字中构造出 ebne 数，请报告这一点。

The input consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 1000$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1 \le n \le 3000$) — the number of digits in the original number.

The second line of each test case contains a non-negative integer number $s$, consisting of $n$ digits.

It is guaranteed that $s$ does not contain leading zeros and the sum of $n$ over all test cases does not exceed $3000$.

输入包含多个测试用例。第一行包含一个整数 $t$（$1 \le t \le 1000$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 3000$），表示原始数字的位数。

每个测试用例的第二行包含一个由 $n$ 位数字组成的非负整数 $s$。

保证 $s$ 不含前导零，且所有测试用例的 $n$ 值之和不超过 $3000$。

For each test case given in the input print the answer in the following format:

• If it is impossible to create an ebne number, print "-1" (without quotes);
• Otherwise, print the resulting number after deleting some, possibly zero, but not all digits. This number should be ebne. If there are multiple answers, you can print any of them. Note that answers with leading zeros or empty strings are not accepted. It's not necessary to minimize or maximize the number of deleted digits.

对于输入中的每个测试用例，请按以下格式输出答案：

• 如果无法构造出一个 ebne 数，则输出 \-1（不带引号）；
• 否则，输出删除若干位（可能为零位，但不能删除所有位）数字后得到的结果数。该数应为 ebne。若存在多个答案，可输出其中任意一个。注意：不允许输出带有前导零的数或空字符串。无需最小化或最大化被删除的数字位数。

In the first test case of the example, $1227$ is already an ebne number (as $1 + 2 + 2 + 7 = 12$, $12$ is divisible by $2$, while in the same time, $1227$ is not divisible by $2$) so we don't need to delete any digits. Answers such as $127$ and $17$ will also be accepted.

In the second test case of the example, it is clearly impossible to create an ebne number from the given number.

In the third test case of the example, there are many ebne numbers we can obtain by deleting, for example, $1$ digit such as $17703$, $77013$ or $17013$. Answers such as $1701$ or $770$ will not be accepted as they are not ebne numbers. Answer $013$ will not be accepted as it contains leading zeroes.

Explanation:

• $1 + 7 + 7 + 0 + 3 = 18$. As $18$ is divisible by $2$ while $17703$ is not divisible by $2$, we can see that $17703$ is an ebne number. Same with $77013$ and $17013$;
• $1 + 7 + 0 + 1 = 9$. Because $9$ is not divisible by $2$, $1701$ is not an ebne number;
• $7 + 7 + 0 = 14$. This time, $14$ is divisible by $2$ but $770$ is also divisible by $2$, therefore, $770$ is not an ebne number.

In the last test case of the example, one of many other possible answers is given. Another possible answer is: 222373204424185217171912 $\rightarrow$ 22237320442418521717191 (delete the last digit).

在示例的第一个测试用例中，$1227$ 本身已是一个 ebne 数（因为 $1 + 2 + 2 + 7 = 12$，而 $12$ 能被 $2$ 整除，同时 $1227$ 不能被 $2$ 整除），因此无需删除任何数字。类似 $127$ 和 $17$ 的答案也同样可接受。

在示例的第二个测试用例中，显然无法从给定数字构造出一个 ebne 数。

在示例的第三个测试用例中，通过删除若干位数字（例如仅删去 $1$ 位），我们可以得到许多 ebne 数，例如 $17703$、$77013$ 或 $17013$。而像 $1701$ 或 $770$ 这样的答案则不可接受，因为它们不是 ebne 数；答案 $013$ 同样不可接受，因为它含有前导零。

解释：

• $1 + 7 + 7 + 0 + 3 = 18$。由于 $18$ 能被 $2$ 整除，而 $17703$ 不能被 $2$ 整除，可知 $17703$ 是一个 ebne 数；同理，$77013$ 和 $17013$ 也是 ebne 数；
• $1 + 7 + 0 + 1 = 9$。由于 $9$ 不能被 $2$ 整除，故 $1701$ 不是 ebne 数；
• $7 + 7 + 0 = 14$。此时 $14$ 能被 $2$ 整除，但 $770$ 也能被 $2$ 整除，因此 $770$ 不是 ebne 数。

在示例的最后一个测试用例中，给出了众多可能答案中的一个。另一个可能的答案是：
222373204424185217171912 $\rightarrow$ 22237320442418521717191（删去最后一位数字）。