CF2053B Outstanding Impressionist

If it was so, then let's make it a deal... — MayDay, [Gentleness](https://www.youtube.com/watch?v=mtAc_bMYBsM&list=PLj6NQzHFCvkHKIm0Vnk9LH3odqTIBRZ1Q&index=15) Even 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.

Each 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 $ .

For 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.

In 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.