A tree is a connected undirected graph without cycles. Note that in this problem, we are talking about not rooted trees.

You are given four positive integers $$$n, d_{12}, d_{23}$$$ and $$$d_{31}$$$. Construct a tree such that:

it contains $$$n$$$ vertices numbered from $$$1$$$ to $$$n$$$,
the distance (length of the shortest path) from vertex $$$1$$$ to vertex $$$2$$$ is $$$d_{12}$$$,
distance from vertex $$$2$$$ to vertex $$$3$$$ is $$$d_{23}$$$,
the distance from vertex $$$3$$$ to vertex $$$1$$$ is $$$d_{31}$$$.

Output any tree that satisfies all the requirements above, or determine that no such tree exists.

Input

The first line of the input contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$) —the number of test cases in the test.

This is followed by $$$t$$$ test cases, each written on a separate line.

Each test case consists of four positive integers $$$n, d_{12}, d_{23}$$$ and $$$d_{31}$$$ ($$$3 \le n \le 2\cdot10^5; 1 \le d_{12}, d_{23}, d_{31} \le n-1$$$).

It is guaranteed that the sum of $$$n$$$ values for all test cases does not exceed $$$2\cdot10^5$$$.

Output

For each test case, print YES if the suitable tree exists, and NO otherwise.

If the answer is positive, print another $$$n-1$$$ line each containing a description of an edge of the tree — a pair of positive integers $$$x_i, y_i$$$, which means that the $$$i$$$th edge connects vertices $$$x_i$$$ and $$$y_i$$$.

The edges and vertices of the edges can be printed in any order. If there are several suitable trees, output any of them.

Build a Tree and That Is It

Examples