[Solution] NIT Destroys the Universe Codeforces Solution

[Solution] NIT Destroys the Universe Codeforces Solution

B. NIT Destroys the Universe

time limit per test

2 seconds

memory limit per test

512 megabytes

input

standard input

output

standard output

For a collection of integers S$S$, define mex(S)$\mathrm{mex}(S)$ as the smallest non-negative integer that does not appear in S$S$.

NIT, the cleaver, decides to destroy the universe. He is not so powerful as Thanos, so he can only destroy the universe by snapping his fingers several times.

The universe can be represented as a 1-indexed array a$a$ of length n$n$. When NIT snaps his fingers, he does the following operation on the array:

• He selects positive integers l$l$ and r$r$ such that 1≤l≤r≤n$1\le l\le r\le n$. Let w=mex({al,al+1,…,ar})$w=\mathrm{mex}(\{a_l,a_{l+1},\dots ,a_r\})$. Then, for all l≤i≤r$l\le i\le r$, set ai$a_i$ to w$w$.

We say the universe is destroyed if and only if for all 1≤i≤n$1\le i\le n$, ai=0$a_i=0$ holds.

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Find the minimum number of times NIT needs to snap his fingers to destroy the universe. That is, find the minimum number of operations NIT needs to perform to make all elements in the array equal to 0$0$.

Input

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Maximum Product? Codeforces Solution

Each test contains multiple test cases. The first line contains the number of test cases t$t$ (1≤t≤104$1\le t\le {10}^4$). Description of the test cases follows.

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

The second line of each test case contains n$n$ integers a1$a_1$, a2$a_2$, …$\dots$, an$a_n$ (0≤ai≤109$0\le a_i\le {10}^9$).

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, print one integer — the answer to the problem.