CF1617C Paprika and Permutation 题解 贪心

Paprika and Permutation

传送门

Paprika loves permutations. She has an array $a_1,a_2,\dots ,a_n$. She wants to make the array a permutation of integers $1$ to $n$.

In order to achieve this goal, she can perform operations on the array. In each operation she can choose two integers $i$ ($1\le i\le n$) and $x$ ($x>0$), then perform $a_i:=a_i\mathrm{mod}x$ (that is, replace $a_i$ by the remainder of $a_i$ divided by $x$). In different operations, the chosen $i$ and $x$ can be different.

Determine the minimum number of operations needed to make the array a permutation of integers $1$ to $n$. If it is impossible, output $-1$.

A permutation is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ($2$ appears twice in the array) and $[1,3,4]$ is also not a permutation ($n=3$ but there is $4$ in the array).

Input

Each test contains multiple test cases. The first line contains a single integer $t$ ($1\le t\le 10^4$) — the number of test cases. Description of the test cases follows.

The first line of each test case contains an integer $n$ ($1\le n$