Given an array \(a_1,a_2,...,a_n\) which means the degree of nodes.
Satori wants to know if there is an undirected graph/a simple undirected graph/a tree whose sequence of degrees = array a.
The first line contains an integer \(n(1\le n\le100000)\), i.e. the number of nodes.
Then one line follows. It contains n integers \(a_i\le 10000000\), which means the degree of node i is \(a_i\).
The first line print "YES"(without quotes) if there is an undirected graph whose sequence of degrees = array a, and "NO"(without quotes) otherwise.
The second line print"YES"(without quotes) if there is a simple undirected graph whose sequence of degrees = array a, and "NO"(without quotes) otherwise.
The third line print"YES"(without quotes) if there is a tree whose sequence of degrees = array a, and "NO"(without quotes) otherwise.