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 $4$ .