Serena has arranged for herself and her family members to come together for dinner at your restaurant! You have arranged the ~N~ members of the family, which includes Serena herself, to sit around a circular table. Conveniently, the family members are numbered from ~0~ to ~N-1~, and sit in such a way that the ~i~-th family member sits adjacent to the ~[(i-1) \bmod N]~-th and ~[(i+1) \bmod N]~-th family member. Having prepared well in advance, you know that the ~i~-th family member would like to be served a total of exactly ~a_i~ dishes. Now, the task that remains is to serve the dishes to Serena's family. To do so, you send a waiter out every minute to serve one dish to exactly two adjacent members around the table.

Determine a sequence of operations to satisfy Serena's family, or gingerly tell them that it is not possible to do so.

Input Specification

The first line contains the integer ~N~, the size of Serena's family.
The next line contains ~N~ integers ~a_0, a_1, \dots, a_{N-1}~, the number of dishes that are to be served to each family member.

Output Specification

If it is possible to satisfy Serena's family, output YES on a single line. Then, output the integer ~M~, the time required in minutes, on a single line. Then, output ~M~ lines, each containing two spaced-separated integers ~x~ and ~y~ (~x \ne y~, ~x~ adjacent to ~y~, ~0 \le x, y < N~). The ~j~-th of these ~M~ lines denotes that a waiter should serve the ~x~-th and the ~y~-th family member simultaneously on the ~j~-th minute.

Otherwise, output NO on a single line.

Constraints

~3 \le N \le 1\,000\,000~
~0 \le a_i \le 1\,000\,000~
The sum of all ~a_i~ does not exceed ~1\,000\,000~.

Sample Input 1

5
3 2 2 0 3

Sample Output 1

YES
5
0 4
4 0
1 2
1 2
4 0

Sample Input 2

3
1337 1337 1337

Sample Output 2

NO