Hasan Jaddouh has invented a new algorithm for generating permutations this algorithm takes an array with length N as input and generate a permutation with length N from this array.

The array must satisfy (1 ≤ Ai ≤ i) in order for the resulting array to be a permutation. Here is the pseudo code of the algorithm:

read N
for i=1 to N do
    read A[i]
for i=1 to N do
    for j=1 to i-1 do
        if A[j] >= A[i] do
            A[j] = A[j]+1
for i=1 to N do
    print A[i]

but unfortunately for Hasan Jaddouh, his algorithm is too slow for big arrays so he asked you to help him to find a fast way to implement his algorithm.

your program should read input same as the pseudocode and output the new array.

Input

first line contains integer N (1 ≤ N ≤ 10⁵).

second line contains N integers separated by spaces each integer is between 1 and 10⁹ inclusive.

Note: in order for Hasan Jaddouh's algorithm to work and generate a permutation the constraint (1 ≤ Ai ≤ i) must be satisfied but to make this problem harder this constraint is not guaranteed so it's also not necessary that the output is a permutation.

Output

Output N integers separated by spaces, the new array after applying Hasan Jaddouh's algorithm.

Example

Input:
4
4 2 1 3

Output:
7 4 1 3