You are given an array (a) of distinct integers. In one operation, you may either: choose a nonempty prefix (^{\text{∗}}) of (a) and replace it with its minimum value, or choose a nonempty suffix (^{\text{†}}) of (a) and replace it with its maximum value. Note that you may choose the entire array (a). For each element (a_i), determine if there exists some sequence of operations to transform (a) into (a_i); that is, make the array (a) consist of only one element, which is (a_i). Output your answer as a binary string of length (n), where the (i)-th character is (1) if there exists a sequence to transform (a) into (a_i), and (0) otherwise. (^{\text{∗}})A prefix of an array is a subarray consisting of the first (k) elements of the array, for some integer (k). (^{\text{†}})A suffix of an array is a subarray consisting of the last (k) elements of the array, for some integer (k). The first line contains an integer (t) ((1 \leq t \leq 10^4)) — the number of test cases. The first line of each test case contains one integer (n) ((2 \leq n \leq 2\cdot 10^5)) — the size of the array (a). The second line of each test case contains (n) integers, (a_1,a_2,\dots,a_n) ((1 \leq a_i \leq 10^6)). It is guaranteed that all (a_i) are distinct. It is guaranteed that the sum of (n) over all test cases does not exceed (2\cdot 10^5). For each test case, output a binary string of length (n) — the (i)-th character should be (1) if there exists a sequence of operations as described above, and (0) otherwise. In the first sample, you can first choose the prefix of size (3). Then the array is transformed into 1 4 7 2 Next, you can choose the suffix of size (2). Then the array is transformed into 1 4 7 Finally, you can choose the prefix of size (3). Then the array is transformed into 1 So we see that it is possible to trans