Problem Statement

There are $N$ houses on a number line. The coordinate of the $i$-th house is $A_i$, and each house has 2 children.
Of the children of house $i$, one moves $L_i$ in the negative direction along the number line and the other moves $R_i$ in the positive direction, handing out sweets to the houses they pass along the way.
Here, for each $i$, if a house exists at coordinate $A_i - L_i$ or $A_i + R_i$, the children of house $i$ are considered to have passed that house.
In other words, the children of house $i$ give sweets to the houses located in $[A_i-L_i, A_i+R_i]$.
How many pairs ( $i$ , $j$ ) ( $i < j$ ) are there such that house $i$ receives sweets from the children of house $j$ and house $j$ receives sweets from the children of house $i$?
Assume that the children of each house have sufficiently many sweets.

(Note) It has been confirmed that AC is achievable with C++ and PyPy3 (1823ms).

Input

$N$
$A_1 \ A_2 \cdots A_N$
$L_1 \ R_1$
$L_2 \ R_2$
$\vdots$
$L_N \ R_N$

$N$ , $A_i$ , $L_i$ , $R_i$ are integers satisfying the following.
$2 \le N \le 3 \times 10^5$
$0 \le A_1 < A_2 < \cdots < A_N \le 10^9$
$0 \le L_i,R_i \le 10^9$

Output

Output the number of $(i,j)\in \{1,2,\dots,N\}^2, i < j$ such that house $i$ receives sweets from the children of house $j$ and house $j$ receives sweets from the children of house $i$.
Note that the answer may not fit in a 32-bit integer type.
Print a newline at the end.

Sample

4
1 2 4 7
3 5
0 3
3 4
2 2

2

2
0 3
1 2
5 4

0

6
1 2 3 4 5 9
1 10
7 3
5 6
3 4
3 9
3 0

9