CF1852E.Rivalries

Ntarsis has an array $a$ of length $n$.

The power of a subarray $a_l \dots a_r$ ($1 \leq l \leq r \leq n$) is defined as:

• The largest value $x$ such that $a_l \dots a_r$ contains $x$ and neither $a_1 \dots a_{l-1}$ nor $a_{r+1} \dots a_n$ contains $x$.
• If no such $x$ exists, the power is $0$.

Call an array $b$ a rival to $a$ if the following holds:

• The length of both $a$ and $b$ are equal to some $n$.
• Over all $l, r$ where $1 \leq l \leq r \leq n$, the power of $a_l \dots a_r$ equals the power of $b_l \dots b_r$.
• The elements of $b$ are positive.

Ntarsis wants you to find a rival $b$ to $a$ such that the sum of $b_i$ over $1 \leq i \leq n$ is maximized. Help him with this task!

Ntarsis 有一个长度为 $n$ 的数组 $a$。

子数组 $a_l \dots a_r$（其中 $1 \leq l \leq r \leq n$）的力量值（power）定义如下：

• 最大的值 $x$，使得 $x$ 出现在 $a_l \dots a_r$ 中，但不出现在 $a_1 \dots a_{l-1}$ 中，也不出现在 $a_{r+1} \dots a_n$ 中；
• 若不存在这样的 $x$，则该子数组的力量值为 $0$。

若数组 $b$ 满足以下条件，则称其为 $a$ 的一个对手数组（rival）：

• $a$ 与 $b$ 的长度均为某个 $n$；
• 对所有满足 $1 \leq l \leq r \leq n$ 的 $l, r$，子数组 $a_l \dots a_r$ 的力量值等于子数组 $b_l \dots b_r$ 的力量值；
• $b$ 的所有元素均为正整数。

Ntarsis 希望你为 $a$ 找到一个对手数组 $b$，使得 $\sum_{i=1}^{n} b_i$ 最大。请帮助他完成这项任务！

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^5$). The description of the test cases follows.

The first line of each test case has a single integer $n$ ($1 \leq n \leq 10^5$).

The next line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 10^9$).

It is guaranteed that the sum of $n$ across all test cases does not exceed $2 \cdot 10^5$.

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 10^5$）。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 $n$（$1 \leq n \leq 10^5$）。

下一行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$1 \leq a_i \leq 10^9$）。

保证所有测试用例中 $n$ 的总和不超过 $2 \cdot 10^5$。

For each test case, output $n$ integers $b_1, b_2, \ldots, b_n$ — a valid rival to $a$ such that $b_1 + b_2 + \cdots + b_n$ is maximal.

If there exist multiple rivals with the maximum sum, output any of them.

对于每个测试用例，输出 $n$ 个整数 $b_1, b_2, \ldots, b_n$ —— 这是一个关于 $a$ 的合法对手序列，且满足 $b_1 + b_2 + \cdots + b_n$ 的值最大。

若存在多个具有最大和的合法对手序列，则输出其中任意一个即可。

For the first test case, one rival with the maximal sum is $[2, 4, 2, 3, 3]$.

$[2, 4, 2, 3, 3]$ can be shown to be a rival to $[1, 4, 1, 3, 3]$.

All possible subarrays of $a$ and $b$ and their corresponding powers are listed below:

• The power of $a[1:1] = [1] = 0$, the power of $b[1:1] = [2] = 0$.
• The power of $a[1:2] = [1, 4] = 4$, the power of $b[1:2] = [2, 4] = 4$.
• The power of $a[1:3] = [1, 4, 1] = 4$, the power of $b[1:3] = [2, 4, 2] = 4$.
• The power of $a[1:4] = [1, 4, 1, 3] = 4$, the power of $b[1:4] = [2, 4, 2, 3] = 4$.
• The power of $a[1:5] = [1, 4, 1, 3, 3] = 4$, the power of $b[1:5] = [2, 4, 2, 3, 3] = 4$.
• The power of $a[2:2] = [4] = 4$, the power of $b[2:2] = [4] = 4$.
• The power of $a[2:3] = [4, 1] = 4$, the power of $b[2:3] = [4, 2] = 4$.
• The power of $a[2:4] = [4, 1, 3] = 4$, the power of $b[2:4] = [4, 2, 3] = 4$.
• The power of $a[2:5] = [4, 1, 3, 3] = 4$, the power of $b[2:5] = [4, 2, 3, 3] = 4$.
• The power of $a[3:3] = [1] = 0$, the power of $b[3:3] = [2] = 0$.
• The power of $a[3:4] = [1, 3] = 0$, the power of $b[3:4] = [2, 3] = 0$.
• The power of $a[3:5] = [1, 3, 3] = 3$, the power of $b[3:5] = [2, 3, 3] = 3$.
• The power of $a[4:4] = [3] = 0$, the power of $b[4:4] = [3] = 0$.
• The power of $a[4:5] = [3, 3] = 3$, the power of $b[4:5] = [3, 3] = 3$.
• The power of $a[5:5] = [3] = 0$, the power of $b[5:5] = [3] = 0$.

It can be shown there exists no rival with a greater sum than $2 + 4 + 2 + 3 + 3 = 14$.

对于第一个测试用例，一个具有最大元素和的对手数组是 $[2, 4, 2, 3, 3]$。

可以验证 $[2, 4, 2, 3, 3]$ 是 $[1, 4, 1, 3, 3]$ 的一个对手数组。

数组 $a$ 和 $b$ 的所有可能子数组及其对应“能量值”（power）如下所列：

• $a[1:1] = [1]$ 的能量值为 $0$，$b[1:1] = [2]$ 的能量值为 $0$。
• $a[1:2] = [1, 4]$ 的能量值为 $4$，$b[1:2] = [2, 4]$ 的能量值为 $4$。
• $a[1:3] = [1, 4, 1]$ 的能量值为 $4$，$b[1:3] = [2, 4, 2]$ 的能量值为 $4$。
• $a[1:4] = [1, 4, 1, 3]$ 的能量值为 $4$，$b[1:4] = [2, 4, 2, 3]$ 的能量值为 $4$。
• $a[1:5] = [1, 4, 1, 3, 3]$ 的能量值为 $4$，$b[1:5] = [2, 4, 2, 3, 3]$ 的能量值为 $4$。
• $a[2:2] = [4]$ 的能量值为 $4$，$b[2:2] = [4]$ 的能量值为 $4$。
• $a[2:3] = [4, 1]$ 的能量值为 $4$，$b[2:3] = [4, 2]$ 的能量值为 $4$。
• $a[2:4] = [4, 1, 3]$ 的能量值为 $4$，$b[2:4] = [4, 2, 3]$ 的能量值为 $4$。
• $a[2:5] = [4, 1, 3, 3]$ 的能量值为 $4$，$b[2:5] = [4, 2, 3, 3]$ 的能量值为 $4$。
• $a[3:3] = [1]$ 的能量值为 $0$，$b[3:3] = [2]$ 的能量值为 $0$。
• $a[3:4] = [1, 3]$ 的能量值为 $0$，$b[3:4] = [2, 3]$ 的能量值为 $0$。
• $a[3:5] = [1, 3, 3]$ 的能量值为 $3$，$b[3:5] = [2, 3, 3]$ 的能量值为 $3$。
• $a[4:4] = [3]$ 的能量值为 $0$，$b[4:4] = [3]$ 的能量值为 $0$。
• $a[4:5] = [3, 3]$ 的能量值为 $3$，$b[4:5] = [3, 3]$ 的能量值为 $3$。
• $a[5:5] = [3]$ 的能量值为 $0$，$b[5:5] = [3]$ 的能量值为 $0$。

可以证明，不存在元素和大于 $2 + 4 + 2 + 3 + 3 = 14$ 的对手数组。