B'Dmitry has n segments of different colors on the coordinate axis Ox . Each segment is characterized by three integers l_i , r_i and c_i ( 1 <= l_i <= r_i <= 10^9, 1 <= c_i <= n ), where l_i and r_i are are the coordinates of the ends of the i -th segment, and c_i is its color. Dmitry likes to find the minimum distances between segments. However, he considers pairs of segments of the same color uninteresting. Therefore, he wants to know for each segment the distance from this segment to the nearest differently colored segment. The distance between two segments is the minimum of the distances between a point of the first segment and a point of the second segment. In particular, if the segments intersect, then the distance between them is equal to 0 . For example, Dmitry has 5 segments: The first line of the input contains an integer t ( 1 <= t <= 10^4 ) -- the number of test cases in the test. The descriptions of the test cases follow. The first line of description of each test case contains one integer n ( 2 <= n <= 2 cdot 10^5 ) -- the number of segments. The next n lines contain descriptions of the segments. Each segment is described by three integers l_i , r_i and c_i ( 1 <= l_i <= r_i <= 10^9, 1 <= c_i <= n ) -- coordinates of the left and right ends of i -th segment, as well as the color of this segment. It is guaranteed that there are at least 2 segments of different colors. It is guaranteed that the sum of n over all test cases does not exceed 2 cdot 10^5 . For each test case, on a separate line print n integers, where the i -th number is equal to the distance from the i -th segment to the nearest segment of a different color. In the first test case of the first sample there is only one segment of color 2 , and all other segments have color 1 . Therefore, for segments of co'...