AT_abc388_d [ABC388D] Coming of Age Celebration

On a certain planet, there are $ N $ aliens, all of whom are minors. The $ i $ -th alien currently has $ A_i $ stones, and will become an adult exactly $ i $ years later. When someone becomes an adult on this planet, every **adult** who has at least one stone gives exactly one stone as a congratulatory gift to the alien who has just become an adult. Find how many stones each alien will have after $ N $ years. Assume that no new aliens will be born in the future.

The input is given from Standard Input in the following format: > $ N $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $

Let $ B_i $ be the number of stones owned by the $ i $ -th alien after $ N $ years. Print $ B_1, B_2, \ldots, B_N $ in this order, separated by spaces.

### Sample Explanation 1 Let $ C_i $ be the number of stones that the $ i $ -th alien has at a given time. Initially, $ (C_1, C_2, C_3, C_4) = (5, 0, 9, 3) $ . After $ 1 $ year, $ (C_1, C_2, C_3, C_4) = (5, 0, 9, 3) $ . After $ 2 $ years, $ (C_1, C_2, C_3, C_4) = (4, 1, 9, 3) $ . After $ 3 $ years, $ (C_1, C_2, C_3, C_4) = (3, 0, 11, 3) $ . After $ 4 $ years, $ (C_1, C_2, C_3, C_4) = (2, 0, 10, 5) $ . ### Constraints - $ 1 \leq N \leq 5 \times 10^5 $ - $ 0 \leq A_i \leq 5 \times 10^5 $ - All input values are integers.