Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Maximum Diameter Graph

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputGraph constructive problems are back! This time the graph you are asked to build should match the following properties.

The graph is connected if and only if there exists a path between every pair of vertices.

The diameter (aka "longest shortest path") of a connected undirected graph is the maximum number of edges in the shortest path between any pair of its vertices.

The degree of a vertex is the number of edges incident to it.

Given a sequence of $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ construct a connected undirected graph of $$$n$$$ vertices such that:

- the graph contains no self-loops and no multiple edges;
- the degree $$$d_i$$$ of the $$$i$$$-th vertex doesn't exceed $$$a_i$$$ (i.e. $$$d_i \le a_i$$$);
- the diameter of the graph is maximum possible.

Output the resulting graph or report that no solution exists.

Input

The first line contains a single integer $$$n$$$ ($$$3 \le n \le 500$$$) — the number of vertices in the graph.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le n - 1$$$) — the upper limits to vertex degrees.

Output

Print "NO" if no graph can be constructed under the given conditions.

Otherwise print "YES" and the diameter of the resulting graph in the first line.

The second line should contain a single integer $$$m$$$ — the number of edges in the resulting graph.

The $$$i$$$-th of the next $$$m$$$ lines should contain two integers $$$v_i, u_i$$$ ($$$1 \le v_i, u_i \le n$$$, $$$v_i \neq u_i$$$) — the description of the $$$i$$$-th edge. The graph should contain no multiple edges — for each pair $$$(x, y)$$$ you output, you should output no more pairs $$$(x, y)$$$ or $$$(y, x)$$$.

Examples

Input

3 2 2 2

Output

YES 2 2 1 2 2 3

Input

5 1 4 1 1 1

Output

YES 2 4 1 2 3 2 4 2 5 2

Input

3 1 1 1

Output

NO

Note

Here are the graphs for the first two example cases. Both have diameter of $$$2$$$.

$$$d_2 = 2 \le a_2 = 2$$$

$$$d_3 = 1 \le a_3 = 2$$$

$$$d_2 = 4 \le a_2 = 4$$$

$$$d_3 = 1 \le a_3 = 1$$$

$$$d_4 = 1 \le a_4 = 1$$$

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/21/2020 13:55:56 (h1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|