Description:
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.
Input Format:
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 Format:
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.
Note:
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 $$$4$$$.