B. Outstanding Impressionisttime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputIf it was so, then let's make it a deal...— MayDay, GentlenessEven after copying the paintings from famous artists for ten years, unfortunately, Eric is still unable to become a skillful impressionist painter. He wants to forget something, but the white bear phenomenon just keeps hanging over him.Eric still remembers $$$n$$$ pieces of impressions in the form of an integer array. He records them as $$$w_1, w_2, \ldots, w_n$$$. However, he has a poor memory of the impressions. For each $$$1 \leq i \leq n$$$, he can only remember that $$$l_i \leq w_i \leq r_i$$$.Eric believes that impression $$$i$$$ is unique if and only if there exists a possible array $$$w_1, w_2, \ldots, w_n$$$ such that $$$w_i \neq w_j$$$ holds for all $$$1 \leq j \leq n$$$ with $$$j \neq i$$$.Please help Eric determine whether impression $$$i$$$ is unique for every $$$1 \leq i \leq n$$$, independently for each $$$i$$$. Perhaps your judgment can help rewrite the final story.InputEach test contains multiple test cases. The first line of the input contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases. The description of test cases follows.The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 2\cdot 10^5$$$) — the number of impressions.Then $$$n$$$ lines follow, the $$$i$$$-th containing two integers $$$l_i$$$ and $$$r_i$$$ ($$$1 \leq l_i \leq r_i \leq 2\cdot n$$$) — the minimum possible value and the maximum possible value of $$$w_i$$$.It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot 10^5$$$.OutputFor each test case, output a binary string $$$s$$$ of length $$$n$$$: for each $$$1 \leq i \leq n$$$, if impression $$$i$$$ is unique, $$$s_i=\texttt{1}$$$; otherwise, $$$s_i=\texttt{0}$$$. Do not output spaces.ExampleInput521 11 141 31 31 31 363 62 21 21 13 42 273 44 44 41 32 51 42 234 54 45 5Output00
1111
100110
1001111
011
NoteIn the first test case, the only possible array $$$w$$$ is $$$[1, 1]$$$, making neither impression $$$1$$$ nor $$$2$$$ unique (since $$$w_1 = w_2$$$).In the second test case, all impressions can be made unique: For $$$i = 1$$$, we can set $$$w$$$ to $$$[1, 3, 2, 3]$$$, in which $$$w_1 \neq w_2$$$, $$$w_1 \neq w_3$$$, and $$$w_1 \neq w_4$$$; For $$$i = 2$$$, we can set $$$w$$$ to $$$[2, 3, 1, 2]$$$, in which $$$w_2 \neq w_1$$$, $$$w_2 \neq w_3$$$, and $$$w_2 \neq w_4$$$; For $$$i = 3$$$, we can set $$$w$$$ to $$$[1, 1, 3, 1]$$$; For $$$i = 4$$$, we can set $$$w$$$ to $$$[2, 3, 3, 1]$$$. In the third test case, for $$$i = 4$$$, we can set $$$w$$$ to $$$[3, 2, 2, 1, 3, 2]$$$. Thus, impression $$$4$$$ is unique.