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E. Chain Reaction
time limit per test
3 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

There are n monsters standing in a row. The i-th monster has ai health points.

Every second, you can choose one alive monster and launch a chain lightning at it. The lightning deals k damage to it, and also spreads to the left (towards decreasing i) and to the right (towards increasing i) to alive monsters, dealing k damage to each. When the lightning reaches a dead monster or the beginning/end of the row, it stops. A monster is considered alive if its health points are strictly greater than 0.

For example, consider the following scenario: there are three monsters with health equal to [5,2,7], and k=3. You can kill them all in 4 seconds:

  • launch a chain lightning at the 3-rd monster, then their health values are [2,1,4];
  • launch a chain lightning at the 1-st monster, then their health values are [1,1,4];
  • launch a chain lightning at the 3-rd monster, then their health values are [1,1,1];
  • launch a chain lightning at the 3-th monster, then their health values are [1,1,2].

For each k from 1 to max, calculate the minimum number of seconds it takes to kill all the monsters.

Input

The first line contains a single integer n (1 \le n \le 10^5) — the number of monsters.

The second line contains n integers a_1, a_2, \dots, a_n (1 \le a_i \le 10^5) — the health points of the i-th monster.

Output

For each k from 1 to \max(a_1, a_2, \dots, a_n), output the minimum number of seconds it takes to kill all the monsters.

Examples
Input
3
5 2 7
Output
10 6 4 3 2 2 1 
Input
4
7 7 7 7
Output
7 4 3 2 2 2 1 
Input
10
1 9 7 6 2 4 7 8 1 3
Output
17 9 5 4 3 3 3 2 1