Banks

Time Limit: 10 Seconds    Memory Limit: 131072 KB

On Wall Street from Wonderland, we have n  banks, with 10000 > n > 0. Each bank has exactly two  neighbours,  the  left  (L)  and  right  (R)  neighbour.  The  first  bank’s  left  neighbour  is  the  last bank, while the last bank’s right neighbour is the first bank.  Each bank i(n>i≥0)  has a capital kwith  32000>k>-32000.  The  entire  capital  of  all  banks  put  together  is  known  to  be  positive. Whenever some capital kof bank i is negative, the Bank Fairy can do a magic move and turn the capital into a positive one. For instance, if  ki=-7, after the magic move,  k=7.  Unfortunately, the magic move has consequences for both neighbours of bank  i. Each sees  its  capital reduced with the absolute value of the capital of bank i. For instance if bank  L  has capital k=5  and bank R has capital k=11, then after the magic move k=-2 and kR=4.

Which is the minimal number of magic moves which the Bank Fairy has to do in order to make the capital of all banks greater than or equal to 0?

Input

On the first input line, we have the number n of banks. On the  second input line, we have the capitals  ki(n>i≥0)  of  all  banks,  in  the  order  in  which  they  are  found  on  Wall  Street  from Wonderland. Each capital is separated by a single whitespace from the next one, except for the final capital which is directly followed by the newline character.

Output

The output contains a single line with the value of the minimal number of magic moves.

```4
1 -2 -1 3```

`9`
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