CF1725L Lemper Cooking Competition

Pak Chanek is participating in a lemper cooking competition. In the competition, Pak Chanek has to cook lempers with $ N $ stoves that are arranged sequentially from stove $ 1 $ to stove $ N $ . Initially, stove $ i $ has a temperature of $ A_i $ degrees. A stove can have a negative temperature. Pak Chanek realises that, in order for his lempers to be cooked, he needs to keep the temperature of each stove at a non-negative value. To make it happen, Pak Chanek can do zero or more operations. In one operation, Pak Chanek chooses one stove $ i $ with $ 2 \leq i \leq N-1 $ , then: 1. changes the temperature of stove $ i-1 $ into $ A_{i-1} := A_{i-1} + A_{i} $ , 2. changes the temperature of stove $ i+1 $ into $ A_{i+1} := A_{i+1} + A_{i} $ , and 3. changes the temperature of stove $ i $ into $ A_i := -A_i $ . Pak Chanek wants to know the minimum number of operations he needs to do such that the temperatures of all stoves are at non-negative values. Help Pak Chanek by telling him the minimum number of operations needed or by reporting if it is not possible to do.

The first line contains a single integer $ N $ ( $ 1 \le N \le 10^5 $ ) — the number of stoves. The second line contains $ N $ integers $ A_1, A_2, \ldots, A_N $ ( $ -10^9 \leq A_i \leq 10^9 $ ) — the initial temperatures of the stoves.

Output an integer representing the minimum number of operations needed to make the temperatures of all stoves at non-negative values or output $ -1 $ if it is not possible.

For the first example, a sequence of operations that can be done is as follows: - Pak Chanek does an operation to stove $ 3 $ , $ A = [2, -2, 1, 4, 2, -2, 9] $ . - Pak Chanek does an operation to stove $ 2 $ , $ A = [0, 2, -1, 4, 2, -2, 9] $ . - Pak Chanek does an operation to stove $ 3 $ , $ A = [0, 1, 1, 3, 2, -2, 9] $ . - Pak Chanek does an operation to stove $ 6 $ , $ A = [0, 1, 1, 3, 0, 2, 7] $ . There is no other sequence of operations such that the number of operations needed is fewer than $ 4 $ .