Making Mexes

문제

You are given an array $aa$ of $NN$ non-negative integers $a_1,a_2,\dots ,a_{N}a\_1,\; a\_2,\; \backslash dots,\; a\_N$ ($1\le N\le 2\cdot {10}^5,0\le a_i\le N1\backslash le\; N\backslash le\; 2\backslash cdot\; 10^5,\; 0\backslash le\; a\_i\backslash le\; N$). In one operation, you can change any element of $aa$ to any non-negative integer.

The mex of an array is the minimum non-negative integer that it does not contain. For each $ii$ in the range $00$ to $NN$ inclusive, compute the minimum number of operations you need in order to make the mex of $aa$ equal $ii$.

입력

The first line contains $NN$.

The next line contains $a_1,a_2,\dots ,a_{N}a\_1,a\_2,\backslash dots,\; a\_N$.

출력

For each $ii$ in the range $00$ to $NN$, output the minimum number of operations for $ii$ on a new line. Note that it is always possible to make the mex of $aa$ equal to any $ii$ in the range $00$ to $NN$.