279. Bipermutations
Time limit per test: 0.25
second(s)
Memory limit: 65536
kilobytes
input: standard
output: standard
A
of order
n is a linear order
of 2n objects
satisfying the following conditions:
For each i such that 1≤ i≤ n holds For each i and j such that 1≤ i,j≤ n holds .
Let
(b_{ii} is undefined). Let a(i) be the number of such j that . You are given integers a_{1},a_{2},..., a_{n}. You have to find any bipermutation such that a(i)=a_{i} for all i.
Input
The first line of the input contains single integer n (1≤ n≤ 1000). The next line contains the numbers a_{1},...,a_{n}.
Output
If there is no solution, the only line of the output must contain single word 'NO' (without quotes). Otherwise the first line of the output must contain single word 'YES' (without quotes); the rest of the output must contain the objects ordered with respect to the bipermutation ( is output as i).
Example(s)
sample input

sample output

9
2 0 3 0 4 8 1 5 4

YES
6 8 9 6 5 3 8 9 7 5 1 4 3 7 2 1 4 2

Hint: If and , then .
Novosibirsk SU Contest #2, by Novosibirsk Team #1