[Solution] Making Towers Codeforces Solution

B. Making Towers

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

You have a sequence of n$n$ colored blocks. The color of the i$i$-th block is ci$c_i$, an integer between 1$1$ and n$n$.

You will place the blocks down in sequence on an infinite coordinate grid in the following way.

1. Initially, you place block 1$1$ at (0,0)$(0,0)$.
2. For 2≤i≤n$2\le i\le n$, if the (i−1)$(i-1)$-th block is placed at position (x,y)$(x,y)$, then the i$i$-th block can be placed at one of positions (x+1,y)$(x+1,y)$, (x−1,y)$(x-1,y)$, (x,y+1)$(x,y+1)$ (but not at position (x,y−1)$(x,y-1)$), as long no previous block was placed at that position.

A tower is formed by s$s$ blocks such that they are placed at positions (x,y),(x,y+1),…,(x,y+s−1)$(x,y),(x,y+1),\dots ,(x,y+s-1)$ for some position (x,y)$(x,y)$ and integer s$s$. The size of the tower is s$s$, the number of blocks in it. A tower of color r$r$ is a tower such that all blocks in it have the color r$r$.

For each color r$r$ from 1$1$ to n$n$, solve the following

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 problem independently:

• Find the maximum size of a tower of color r$r$ that you can form by placing down the blocks according to the rules.

Input

The first line contains a single integer t$t$ (1≤t≤104$1\le t\le {10}^4$) — the number of test cases.

The first line of each test case contains a single integer n$n$ (1≤n≤105$1\le n\le {10}^5$).

The second line of each test case contains n$n$ integers c1,c2,…,cn$c_1,c_2,\dots ,c_n$ (1≤ci≤n$1\le c_i\le n$).

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It is guaranteed that the sum of n$n$ over all test cases does not exceed 2⋅105$2\cdot {10}^5$.

Output

For each test case, output n$n$ integers. The r$r$-th of them should be the maximum size of an tower of color r$r$ you can form by following the given rules. If you cannot form any tower of color r$r$, the r$r$-th integer should be 0$0$.