Given an integer $n$, $1 <= n <= 10^5$, and an array $a$ consisting of $n$ elements, figure out if the array is a good array. A good array is defined to be first increasing, then decreasing. Note that an increasing array or decreasing array is a good array. An increasing array is an array such that every next element of every element(that is not the last) has to be greater than or equal to that element. A decreasing array is an array such that every next element of every element(that is not the last) has to be less than or equal to that element.↵
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Example:↵
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Input:↵
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5↵
1 2 4 3 1↵
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Output:↵
YES↵
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Input:↵
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3↵
3 2 1↵
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Output:↵
NOYES↵
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Input:↵
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5↵
1 2 3 4 4↵
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Output:↵
YES↵
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Input:↵
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5 ↵
5 4 2 1 1↵
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Output:↵
YES
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Example:↵
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Input:↵
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5↵
1 2 4 3 1↵
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Output:↵
YES↵
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Input:↵
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3↵
3 2 1↵
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Output:↵
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Input:↵
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5↵
1 2 3 4 4↵
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Output:↵
YES↵
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Input:↵
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5 ↵
5 4 2 1 1↵
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Output:↵
YES