In a mysterious botanical garden, an unusual phenomenon is occurring. Each plant hosts a colony of zombie ants that produce both poison and antidote. The delicate balance between these substances determines the plants' survival.

Each plant contains a specific number of zombie ants. These ants have a peculiar behavior:

• Each ant produces a fixed amount of poison that stays within its host plant.
• Each ant also produces an antidote, but the antidote immediately transfers to the neighboring plant on the right (if such a plant exists).
• The leftmost plant has a special property—it receives an infinite supply of antidote from an underground spring, ensuring its survival.

Each night, a deadly cycle occurs:

• If a plant's poison level (determined by its number of ants) exceeds the antidote it receives from its left neighbor, the plant dies and is removed from the garden.
• After plant deaths, the antidote flow adjusts to the new arrangement before the next night begins.

The first line contains an integer \( n \) \((1 \leq n \leq 10^5)\), the number of plants in the garden. The second line contains \( n \) space-separated integers \( p_1, p_2, \ldots, p_n \), where \( p_i \) \((0 \leq p_i \leq 10^9) \) represents the number of zombie ants in the \( i \)-th plant.

Output a single integer representing the number of nights until plants stop dying.