\(n\) circles are placed in a \(2D\) plane, with radii \(r_1, r_2, ..., r_n\) and centers \(O_1, O_2, ..., O_n\) such that these circles all intersect at a common point \(P\), no arrangement of the set \((O_j, O_i, P)\) is linear and \(r_i \neq r_j\), for all \(i, j\) satisfying \(0 \leq i \leq n\), \(0 \leq j \leq n\) and \(i \neq j\). Given the integers \(m_3, m_4, m_5, ..., m_{n-1}\), where \(m_k\) is the number of points in the plane where \(k\) circles intersect, find the number of sections these circles divide the whole plane into.

** Example:** If \(n = 9\) and \(m_3 = 0, m_4 = 2, m_5 = 0, m_6 = 1, m_7 = 0, m_8 = 0\), this means there are \(9\) circles all sharing a common point \(P\) and there are \(2\) distinct point such that \(4\) circles intersect and \(1\) point such that \(6\) circles intersect. At the other intersections, only \(2\) circles intersect.

##### Input

The first line contains the number \(n\) and the subsequent lines contain \(m_3, m_4, m_5, ..., m_{n-1}\).

- \(5 \leq n \leq 10^7\)
- \(0 \leq m_j\leq 10^5\)

##### Output

Print the total number of distinct sections formed by these circles on the plane.

##### Example 1

**Input:**

```
5
1
0
```

**Output:**

`15`

##### Example 2

**Input:**

```
10
0
2
0
1
0
0
0
```

**Output:**

`40`

##### Explanation

**Input 1:**
Here's a way to construct \(5\) circles that all intersect at the point \(P\), and a point \(B\) where \(3\) circles intersect. If we count the number of sections in the entire plane, we can see there are \(15\) sections.

**Input 2:**
Here's a way to construct \(10\) circles that all intersect at the point \(P\), a point \(B\), \(C\) where \(4\) circles intersect and a point \(D\) where \(6\) circles intersect. If we count the number of sections in the entire plane, we can see there are \(40\) sections.