B"Olya has an array of integers a_1, a_2, ldots, a_n . She wants to split it into tandem repeats. Since it's rarely possible, before that she wants to perform the following operation several (possibly, zero) number of times: insert a pair of equal numbers into an arbitrary position. Help her! More formally: Each test contains multiple test cases. The first line contains a single integer t ( 1 <= t <= 30 ,000 ) -- the number of test cases. Description of the test cases follows. The first line of each test case contains a single integer n ( 1 <= n <= 500 ). The second line contains n integers a_1, a_2, ldots, a_n ( 1 <= a_i <= 10^9 ) -- the initial array. It is guaranteed that the sum of n^2 over all test cases does not exceed 250 ,000 . For each test case print answer in the following format. If you cannot turn the array into a concatenation of tandem repeats, print a single integer -1 . Otherwise print the number of operations q ( 0 <= q <= 2 cdot n^2 ) that you want to do. Then print the descriptions of operations. In each of the following q lines print two integers p and c ( 1 <= c <= 10^9 ), which mean that you insert the integer c twice after p elements of the array. If the length of the array is m before the operation, then the condition 0 <= p <= m should be satisfied. Then you should print any way to split the resulting array into tandem repeats. First, print a single integer d , and then print a sequence t_1, t_2, ldots, t_d of even integers of size d ( d, t_i ge 1 ). These numbers are the lengths of the subsegments from left to right. Note that the size of the resulting array a is m = n + 2 cdot q . The following statements must hold: It can be shown that if the array can be turned into a concatenation of tandem repeats, then there exists a solution satisfying all constraints. If th"...