Given a sequence of integers $( a_1, a_2, \dots, a_n )$ where $( 1 \leq a_i \leq 10^6 )$, count the number of subsequences with indices $( i_1, i_2, \dots, i_k )$ such that:↵
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$ k > 0 $,↵
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$ 1 < i_2 < \dots < i_k \leq n ,$↵
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$ a_{i_1} \leq a_{i_2} \leq \dots \leq a_{i_k} ,$↵
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$ \gcd(a_{i_1}, a_{i_2}, \dots, a_{i_k}) = 1 .$↵
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The first line contains an integer $n $ $(1 \leq n \leq 3 \times 10^5)$, representing the number of elements in the sequence.↵
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The second line contains $ n $ integers $ a_1, a_2, \dots, a_n $ $(1 \leq a_i \leq 10^6)$.↵
↵
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$ k > 0 $,↵
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$ 1 < i_2 < \dots < i_k \leq n ,$↵
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$ a_{i_1} \leq a_{i_2} \leq \dots \leq a_{i_k} ,$↵
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$ \gcd(a_{i_1}, a_{i_2}, \dots, a_{i_k}) = 1 .$↵
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The first line contains an integer $n $ $(1 \leq n \leq 3 \times 10^5)$, representing the number of elements in the sequence.↵
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The second line contains $ n $ integers $ a_1, a_2, \dots, a_n $ $(1 \leq a_i \leq 10^6)$.↵
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