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:
For each k from 1 to max, calculate the minimum number of seconds it takes to kill all the monsters.
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.
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.
35 2 7
10 6 4 3 2 2 1
47 7 7 7
7 4 3 2 2 2 1
101 9 7 6 2 4 7 8 1 3
17 9 5 4 3 3 3 2 1
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