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 PYTHON3):

Solution:
''' Thruth can only be found at one place - THE CODE '''

''' Copyright 2018, SATYAM KUMAR'''
from sys import stdin, stdout
import cProfile, math
from collections import Counter
from bisect import bisect_left,bisect,bisect_right
import itertools
from copy import deepcopy
from fractions import Fraction
import sys, threading
sys.setrecursionlimit(10**6) # max depth of recursion
threading.stack_size(2**27)  # new thread will get stack of such size

printHeap = str()
memory_constrained = False
P = 10**9+7
import sys
sys.setrecursionlimit(10000000)

class Operation:
    def __init__(self, name, function, function_on_equal, neutral_value=0):
        self.name = name
        self.f = function
        self.f_on_equal = function_on_equal
def add_multiple(x, count):
    return x * count
def min_multiple(x, count):
    return x
def max_multiple(x, count):
    return x
sum_operation = Operation("sum", sum, add_multiple, 0)
min_operation = Operation("min", min, min_multiple, 1e9)
max_operation = Operation("max", max, max_multiple, -1e9)
class SegmentTree:
    def __init__(self,
                 array,
                 operations=[sum_operation, min_operation, max_operation]):
        self.array = array
        if type(operations) != list:
            raise TypeError("operations must be a list")
        self.operations = {}
        for op in operations:
            self.operations[op.name] = op
        self.root = SegmentTreeNode(0, len(array) - 1, self)
    def query(self, start, end, operation_name):
        if self.operations.get(operation_name) == None:
            raise Exception("This operation is not available")
        return self.root._query(start, end, self.operations[operation_name])
    def summary(self):
        return self.root.values
    def update(self, position, value):
        self.root._update(position, value)
    def update_range(self, start, end, value):
        self.root._update_range(start, end, value)
    def __repr__(self):
        return self.root.__repr__()
class SegmentTreeNode:
    def __init__(self, start, end, segment_tree):
        self.range = (start, end)
        self.parent_tree = segment_tree
        self.range_value = None
        self.values = {}
        self.left = None
        self.right = None
        if start == end:
            self._sync()
            return
        self.left = SegmentTreeNode(start, start + (end - start) // 2,
                                    segment_tree)
        self.right = SegmentTreeNode(start + (end - start) // 2 + 1, end,
                                     segment_tree)
        self._sync()
    def _query(self, start, end, operation):
        if end < self.range[0] or start > self.range[1]:
            return None
        if start <= self.range[0] and self.range[1] <= end:
            return self.values[operation.name]
        self._push()
        left_res = self.left._query(start, end,
                                    operation) if self.left else None
        right_res = self.right._query(start, end,
                                      operation) if self.right else None
        if left_res is None:
            return right_res
        if right_res is None:
            return left_res
        return operation.f([left_res, right_res])
    def _update(self, position, value):
        if position < self.range[0] or position > self.range[1]:
            return
        if position == self.range[0] and self.range[1] == position:
            self.parent_tree.array[position] = value
            self._sync()
            return
        self._push()
        self.left._update(position, value)
        self.right._update(position, value)
        self._sync()
    def _update_range(self, start, end, value):
        if end < self.range[0] or start > self.range[1]:
            return
        if start <= self.range[0] and self.range[1] <= end:
            self.range_value = value
            self._sync()
            return
        self._push()
        self.left._update_range(start, end, value)
        self.right._update_range(start, end, value)
        self._sync()
    def _sync(self):
        if self.range[0] == self.range[1]:
            for op in self.parent_tree.operations.values():
                current_value = self.parent_tree.array[self.range[0]]
                if self.range_value is not None:
                    current_value = self.range_value
                self.values[op.name] = op.f([current_value])
        else:
            for op in self.parent_tree.operations.values():
                result = op.f(
                    [self.left.values[op.name], self.right.values[op.name]])
                if self.range_value is not None:
                    bound_length = self.range[1] - self.range[0] + 1
                    result = op.f_on_equal(self.range_value, bound_length)
                self.values[op.name] = result
    def _push(self):
        if self.range_value is None:
            return
        if self.left:
            self.left.range_value = self.range_value
            self.right.range_value = self.range_value
            self.left._sync()
            self.right._sync()
            self.range_value = None
    def __repr__(self):
        ans = "({}, {}): {}\n".format(self.range[0], self.range[1],
                                      self.values)
        if self.left:
            ans += self.left.__repr__()
        if self.right:
            ans += self.right.__repr__()
        return ans

def display(string_to_print):
    stdout.write(str(string_to_print) + "\n")

def primeFactors(n): #n**0.5 complex 
    factors = dict()
    for i in range(2,math.ceil(math.sqrt(n))+1):  
        while n % i== 0: 
            if i in factors:
                factors[i]+=1
            else: factors[i]=1
            n = n // i 
    if n>2:
        factors[n]=1
    return (factors)
    
def isprime(n):
    """Returns True if n is prime."""
    if n < 4:
        return True
    if n % 2 == 0:
        return False
    if n % 3 == 0:
        return False
    i = 5
    w = 2
    while i * i <= n:
        if n % i == 0:
            return False
        i += w
        w = 6 - w
    return True

def test_print(*args):
    if testingMode:
        print(args)

def display_list(list1, sep=" "):
    stdout.write(sep.join(map(str, list1)) + "\n")

def get_int():
    return int(stdin.readline().strip())

def get_tuple():
    return map(int, stdin.readline().split())

def get_list():
    return list(map(int, stdin.readline().split()))

memory = dict()
def clear_cache():
    global memory
    memory = dict()
def cached_fn(fn, *args):
    global memory
    if args in memory:
        return memory[args]
    else:
        result = fn(*args)
        memory[args] = result
        return result


# -------------------------------------------------------------- MAIN PROGRAM
TestCases = False
testingMode = False
optimiseForReccursion = False #Can not be used clubbed with TestCases
def comp(li):
    return len(li)

def main():
    n=get_int()
    li = get_list()
    extra = []
    res = []
    hooks_left = []
    used = [] # parallel arrays
    line_len = 0
    for i,ele in enumerate(li):
        if i==0: 
            hooks_left.append(li[i])
            used.append(i)
        else:
            if (ele==1):
                extra.append(i)
            else:
                line_len+=1
                hooks_left[-1]-=1
                hooks_left.append(li[i]-1)
                res.append([used[-1]+1,i+1])
                used.append(i)
    #print(res,extra,hooks_left,used,line_len)
    if (hooks_left[0]>0) and len(extra)>0:
        line_len+=1
        res.append([used[0]+1,extra.pop()+1])
        hooks_left[0]-=1
    if (hooks_left[-1]>0) and len(extra)>0:
        line_len+=1
        res.append([used[-1]+1,extra.pop()+1])
        hooks_left[-1]-=1
    for i,ele in enumerate(hooks_left):
        if ele==0:
            continue
        if len(extra)==0:
            break
        while len(extra)>0 and ele>0:
            res.append([used[i]+1,extra.pop()+1])
            ele-=1
    if len(extra)>0:
        print("NO")
        return
    else:
        print("YES",line_len)
        print(len(res))
        for x in res:
            print(x[0],x[1])
        return

# --------------------------------------------------------------------- END


if TestCases: 
    for _ in range(get_int()): 
        cProfile.run('main()') if testingMode else main() 
else: (cProfile.run('main()') if testingMode else main()) if not optimiseForReccursion else threading.Thread(target=main).start()