Nikyr has started working as a queue manager at the company "Black Contour." He needs to choose the order of servicing customers. There are a total of (n) queues, each initially containing (0) people. In each of the next (n) moments of time, there are two sequential events: New customers arrive in all queues. More formally, at the (j)-th moment of time, the number of people in the (i)-th queue increases by a positive integer (a_{i,j}). Nikyr chooses exactly one of the (n) queues to be served at that moment in time. The number of customers in this queue becomes (0). Let the number of people in the (i)-th queue after all events be (x_i). Nikyr wants MEX(^{\dagger}) of the collection (x_1, x_2, \ldots, x_n) to be as large as possible. Help him determine the maximum value he can achieve with an optimal order of servicing the queues. (^{\dagger})The minimum excluded (MEX) of a collection of integers (c_1, c_2, \ldots, c_k) is defined as the smallest non-negative integer (y) which does not occur in the collection (c). For example: (\operatorname{MEX}(2,2,1)= 0), since (0) does not belong to the array. (\operatorname{MEX}(3,1,0,1) = 2), since (0) and (1) belong to the array, but (2) does not. (\operatorname{MEX}(0,3,1,2) = 4), since (0), (1), (2), and (3) belong to the array, but (4) does not. Each test consists of multiple test cases. The first line contains a single integer (t) ((1 \le t \le 2 \cdot 10^4)) — the number of test cases. The description of the test cases follows. The first line of each test case contains a single integer (n) ((1 \le n \le 300)) — the number of queues and moments of time. The (i)-th of the next (n) lines contains (n) integers (a_{i,1}, a_{i,2}, \ldots, a_{i,n}) ((1 \le a_{i,j} \le 10^9)) — the number of new customers in the (i)-th queue at each moment of time. It is guaranteed