Problem: Graph 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, ..., 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 ≤ 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 ≤ n ≤ 500) — the number of vertices in the graph.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 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 ≤ v_i, u_i ≤ n, v_i ≠ 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.

<image> d_1 = 1 ≤ a_1 = 2

d_2 = 2 ≤ a_2 = 2

d_3 = 1 ≤ a_3 = 2 

<image> d_1 = 1 ≤ a_1 = 1

d_2 = 4 ≤ a_2 = 4

d_3 = 1 ≤ a_3 = 1

d_4 = 1 ≤ a_4 = 1 

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
	public static void main(String[] args) throws IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		PrintWriter out = new PrintWriter(outputStream);
		InputReader in = new InputReader(inputStream);
		//InputStream uinputStream = new FileInputStream("closing.in");
		//InputReader in = new InputReader(uinputStream);
		//PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("closing.out")));
		Task t = new Task();
		t.solve(in, out);
		out.close();
	}
	
	static class Task {
		class BIT{
			int arr[];
			int n;
			public BIT(int a) {
				n=a;
				arr = new int[n];
			}
			int sum(int p) {
				int s=0;
				while(p>0) {
					s+=arr[p];
					p-=p&(-p);
				}
				return s;
			}
			void add(int p, int v) {
				while(p<n) {
					arr[p]+=v;
					p+=p&(-p);
				}
			}
		}
		class DSU{
			int[] arr;
			int[] sz;
			public DSU(int n) {
				arr = new int[n];
				sz = new int[n];
				for(int i=0;i<n;i++) arr[i] = i;
				Arrays.fill(sz, 1);
			}
			public int find(int a) {
				if(arr[a]!=a) arr[a] = find(arr[a]);
				return arr[a];
			}
			public void union(int a, int b) {
				int x = find(a);
				int y = find(b);
				if(x==y) return;
				arr[x] = y;
				sz[y] += sz[x];
			}
			public int size(int x) {
				return sz[find(x)];
			}
		}
		
		class node implements Comparable<node>{
			int id; int av;
			public node(int a, int b) {
				id=a;av=b;
			}
			@Override
			public int compareTo(node t) {
				return this.av-t.av;
			}
		}

		public void solve(InputReader in, PrintWriter out) throws IOException {
			
//			Dumper.print_int_arr(movesToStamp("mda","mdadddaaaa"));
//			Dumper.print_int_arr(movesToStamp("aye","eyeye"));
//			Dumper.print_int_arr(movesToStamp("df","dfdff"));
//			Dumper.print_int_arr(movesToStamp("aye","eyeye"));
//			Dumper.print_int_arr(movesToStamp("oz","ooozz"));
//			Dumper.print_int_arr(movesToStamp("abca","aabcaca"));
//			Dumper.print_int_arr(movesToStamp("cab","cabbb"));
//			Dumper.print_int_arr(movesToStamp("aq","aqaaqaqqqaqqaaq"));
			//int//arr[] = {2,3,6,7,4,12,21,39};
			//int[] arr = {2,3,6,7,4,12,21,39};
			//int arr[] = {4,6,15,35};
			int n = in.nextInt();
			node arr[] = new node[n];
			int dep[] = new int[n];
			
			PriorityQueue<node> q = new PriorityQueue<node>();
			int t=0;
			for(int i=0;i<n;i++) {
				arr[i] = new node(i, in.nextInt());
				q.add(arr[i]);
				t+=arr[i].av;
			}
			if(t<2*n-2) {
				out.println("NO");
				return;
			}
			
			boolean[][] e = new boolean[n][n];
			int re = 0;
			int max = 1;
			node tmp[] = new node[n];
			int p=0;
			while(!q.isEmpty()&&q.peek().av==1) tmp[p++] = q.poll();
			
			node tmp2[] = new node[n];
			int p2=0;
			node pre = null;
			while(!q.isEmpty()) {
				node xx = q.poll();
				if(pre!=null) {
					pre.av--;
					tmp2[p2++] = pre;
					re++;
					xx.av--;
					e[pre.id][xx.id] = true;
					dep[xx.id]+=dep[pre.id]+1;
				}
				pre = xx;
			}
			for(int i:dep) max = Math.max(max, i);
			tmp2[p2] = pre;
			if(p>=1&&tmp2[0].av>0) {
				tmp2[0].av--;				
				p--;			
				e[tmp[p].id][tmp2[0].id] = true;
				max++;
				re++;
			}
			if(p>=1&&p2!=0&&tmp2[p2].av>0) {
				tmp2[p2].av--;
				p--;
				e[tmp[p].id][tmp2[p2].id] = true;
				max++;
				re++;
			}
			for(int i=0;i<p;i++) {
				if(tmp2[p2].av>0) {
					e[tmp[i].id][tmp2[p2].id] = true;
					tmp2[p2].av--;
					re++;			
				}
				if(tmp2[p2].av==0) p2--;				
			}
			
			out.println("YES "+max);
			out.println(re);
			for(int i=0;i<n;i++) {
				for(int j=i+1;j<n;j++) {
					if(e[i][j]||e[j][i]) out.println((i+1)+" "+(j+1));
				}
			}
		}
		
	    public int[] movesToStamp(String stamp, String target) {
	    	int n = stamp.length();
	    	int m = target.length();
	    	char[] s = stamp.toCharArray();
	    	char[] t = target.toCharArray();
	    	ArrayList<Integer> part1 = new ArrayList<Integer>();
	    	ArrayList<Integer> part2 = new ArrayList<Integer>();
	    	ArrayList<Integer> part3 = new ArrayList<Integer>();
	    	int p = target.indexOf(stamp);
            if(p==-1) return new int[] {};
            part1.add(p);
	    	update(t,p,p+stamp.length());
	    	while(true) {
	    		int x = target.indexOf(stamp,p+stamp.length());	    		
	    		if(x==-1) break;
	    		update(t,x,x+stamp.length());
	    		part1.add(0,x);
	    		p=x;
	    	}	    
	    	
	    	TreeSet<Integer> todo = new TreeSet<Integer>(Collections.reverseOrder());
	    	for(int i=0;i<m;i++) if(t[i]!='*') todo.add(i);
	    	
	    	while(true) {
	    		int temp = -1;
	    		for(int i:todo) {
	    			if(i+1<m&&t[i+1]=='*') {
	    				temp = i;
	    				int tmp = stamp.indexOf(t[i]);
	    				if(i-tmp<0) return new int[] {};
	    				part2.add(i-tmp);	    			
	    				t[i]='*';
	    				break;
	    			}
	    		}
	    		if(temp==-1) break;
	    		else todo.remove(temp);
	    	}
	    	
	    	while(!todo.isEmpty()) {
	    		int l = 0; int end = 0;
	    		for(int i:todo) {
	    			end=i;
	    			l = backmatch(s,t,i);
	    			part3.add(i-n+1);	    			
	    			update(t,i-l+1,i);
	    			break;
	    		}
	    		if(l==0) return new int[] {};
	    		else {
	    			for(int j=end-l+1;j<=end;j++)
	    				todo.remove(j);    		
	    		}
	    	}	    	
	    	int[] ret = new int[part1.size()+part2.size()+part3.size()];	
	    	int c=0;
	    	for(int i:part3) {
	    		ret[c++] = i;
	    	}
	    	for(int i:part2) {
	    		ret[c++] = i;
	    	}
	    	for(int i:part1) {
	    		ret[c++] = i;
	    	}	    	
	    	return ret;
	    }
	    public int backmatch(char s[], char t[], int idx) {
	    	int q = s.length-1;
	    	int c = 0;
	    	while(q>0&&idx>0&&s[q]==t[idx]) {
	    		q--;idx--;c++;
	    	}
	    	return c;
	    }
	    public void update(char[] arr, int s, int l) {
	    	for(int i=s;i<l;i++) arr[i] = '*';
	    }
	}
	static class MinHeap<Key> implements Iterable<Key> {
		private int maxN;
		private int n;
		private int[] pq;
		private int[] qp;
		private Key[] keys;
		private Comparator<Key> comparator;
		
		public MinHeap(int capacity){
			if (capacity < 0) throw new IllegalArgumentException();
			this.maxN = capacity;
			n=0;
			pq = new int[maxN+1];
			qp = new int[maxN+1];
			keys = (Key[]) new Object[capacity+1];
			Arrays.fill(qp, -1);
		}
		
		public MinHeap(int capacity, Comparator<Key> c){
			if (capacity < 0) throw new IllegalArgumentException();
			this.maxN = capacity;
			n=0;
			pq = new int[maxN+1];
			qp = new int[maxN+1];
			keys = (Key[]) new Object[capacity+1];
			Arrays.fill(qp, -1);
			comparator = c;
		}			
		public boolean isEmpty()	{ return n==0; 	}
		public int size()			{ return n;		}
		public boolean contains(int i) {
	        if (i < 0 || i >= maxN) throw new IllegalArgumentException();
	        return qp[i] != -1;
		}	
		public int peekIdx() {
	        if (n == 0) throw new NoSuchElementException("Priority queue underflow");
	        return pq[1];		
		}	
		public Key peek(){
			if(isEmpty()) throw new NoSuchElementException("Priority queue underflow");
			return keys[pq[1]];
		}
		public int poll(){
			if(isEmpty()) throw new NoSuchElementException("Priority queue underflow");
			int min = pq[1];
			exch(1,n--);
			down(1);
			assert min==pq[n+1];
			qp[min] = -1;
			keys[min] = null;		
			pq[n+1] = -1;
			return min;
		}
	    public void update(int i, Key key) {
	        if (i < 0 || i >= maxN) throw new IllegalArgumentException();
	        if (!contains(i)) {
	        	this.add(i, key);
	        }else {
	        	keys[i] = key;
	        	up(qp[i]);
	        	down(qp[i]);
	        }
	    }	
		private void add(int i, Key x){
	        if (i < 0 || i >= maxN) throw new IllegalArgumentException();
	        if (contains(i)) throw new IllegalArgumentException("index is already in the priority queue");
	        n++;
	        qp[i] = n;
	        pq[n] = i;
	        keys[i] = x;
	        up(n);
		}
		private void up(int k){
			while(k>1&&less(k,k/2)){
				exch(k,k/2);
				k/=2;
			}
		}
		private void down(int k){
			while(2*k<=n){
				int j=2*k;
				if(j<n&&less(j+1,j)) j++;
				if(less(k,j)) break;
				exch(k,j);
				k=j;
			}
		}
		
		public boolean less(int i, int j){
	        if (comparator == null) {
	            return ((Comparable<Key>) keys[pq[i]]).compareTo(keys[pq[j]]) < 0;
	        }
	        else {
	            return comparator.compare(keys[pq[i]], keys[pq[j]]) < 0;
	        }
		}

		public void exch(int i, int j){
	        int swap = pq[i];
	        pq[i] = pq[j];
	        pq[j] = swap;
	        qp[pq[i]] = i;
	        qp[pq[j]] = j;
		}

		@Override
		public Iterator<Key> iterator() {
			// TODO Auto-generated method stub
			return null;
		}
	}  	

    private static class InputReader
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int zcurChar;
        private int znumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }

        public int read()
        {
            if (znumChars == -1)
                throw new InputMismatchException();
            if (zcurChar >= znumChars)
            {
            	zcurChar = 0;
                try
                {
                    znumChars = stream.read(buf);
                } catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                if (znumChars <= 0)
                    return -1;
            }
            return buf[zcurChar++];
        }

        public int nextInt()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String nextString()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public double nextDouble()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.')
            {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.')
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c))
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public long nextLong()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next()
        {
            return nextString();
        }

        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }    

	static class Dumper {
		static void print_int_arr(int[] arr) {
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print_char_arr(char[] arr) {
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print_double_arr(double[] arr) {
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print_2d_arr(int[][] arr, int x, int y) {
			for (int i = 0; i < x; i++) {
				for (int j = 0; j < y; j++) {
					System.out.print(arr[i][j] + " ");
				}
				System.out.println();
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print_2d_arr(boolean[][] arr, int x, int y) {
			for (int i = 0; i < x; i++) {
				for (int j = 0; j < y; j++) {
					System.out.print(arr[i][j] + " ");
				}
				System.out.println();
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print(Object o) {
			System.out.println(o.toString());
		}

		static void getc() {
			System.out.println("here");
		}
	}
}