Description: It is an interactive problem. Vasya enjoys solving quizzes. He found a strange device and wants to know how it works. This device encrypted with the tree (connected undirected graph without cycles) with $$$n$$$ vertices, numbered with integers from $$$1$$$ to $$$n$$$. To solve this quiz you should guess this tree. Fortunately, this device can make one operation, using which you should guess the cipher. You can give the device an array $$$d_1, d_2, \ldots, d_n$$$ of non-negative integers. On the device, there are $$$n$$$ lamps, $$$i$$$-th of them is connected with $$$i$$$-th vertex of the tree. For all $$$i$$$ the light will turn on the $$$i$$$-th lamp, if there exist such vertex of the tree with number $$$j \neq i$$$ that $$$dist(i, j) \leq d_j$$$. Let's define $$$dist(i, j)$$$ as the distance between vertices $$$i$$$ and $$$j$$$ in tree or number of edges on the simple path between vertices $$$i$$$ and $$$j$$$. Vasya wants to solve this quiz using $$$\leq 80$$$ operations with the device and guess the tree. Help him! Input Format: None Output Format: None Note: It is a picture of the tree which encrypt the device from the first test: It is a table of pairwise distances between vertices in this tree: - If you make operation where $$$d = [0, 0, 0, 0, 0]$$$, no lamp will switch on, because $$$dist(i, j) > 0$$$ for all $$$i \neq j$$$. - If you make operation where $$$d = [1, 1, 2, 0, 2]$$$, all lamps except the lamp connected with the $$$3$$$-rd vertex will switch on. For example, lamp connected with the $$$1$$$-st vertex will switch on, because $$$dist(1, 5) = 1 \leq 2 = d_5$$$. - If you make operation where $$$d = [0, 0, 0, 1, 0]$$$, all lamps except lamps connected with the $$$4$$$-th and $$$5$$$-th vertices will switch on. - If you make operation where $$$d = [0, 1, 0, 0, 1]$$$, only lamps connected with the $$$1$$$-st and $$$4$$$-th vertices will switch on.