CF1667A Make it Increasing

You are given an array $ a $ consisting of $ n $ positive integers, and an array $ b $ , with length $ n $ . Initially $ b_i=0 $ for each $ 1 \leq i \leq n $ . In one move you can choose an integer $ i $ ( $ 1 \leq i \leq n $ ), and add $ a_i $ to $ b_i $ or subtract $ a_i $ from $ b_i $ . What is the minimum number of moves needed to make $ b $ increasing (that is, every element is strictly greater than every element before it)?

The first line contains a single integer $ n $ ( $ 2 \leq n \leq 5000 $ ). The second line contains $ n $ integers, $ a_1 $ , $ a_2 $ , ..., $ a_n $ ( $ 1 \leq a_i \leq 10^9 $ ) — the elements of the array $ a $ .

Print a single integer, the minimum number of moves to make $ b $ increasing.

Example $ 1 $ : you can subtract $ a_1 $ from $ b_1 $ , and add $ a_3 $ , $ a_4 $ , and $ a_5 $ to $ b_3 $ , $ b_4 $ , and $ b_5 $ respectively. The final array will be \[ $ -1 $ , $ 0 $ , $ 3 $ , $ 4 $ , $ 5 $ \] after $ 4 $ moves. Example $ 2 $ : you can reach \[ $ -3 $ , $ -2 $ , $ -1 $ , $ 0 $ , $ 1 $ , $ 2 $ , $ 3 $ \] in $ 10 $ moves.