Problem Statement

Takahashi and Aoki are running on a straight running course. This course has a start point, and N water stations are aligned in a straight line ahead of it, numbered 1, 2, \ldots, N in increasing order of distance from the start point. Water station N is the goal of this course.

The distance from the start point to water station 1, as well as the distance between any two adjacent water stations, is 1. Takahashi runs at a constant speed of V per second, and Aoki runs at a constant speed of W per second.

Takahashi and Aoki may stop at each water station to hydrate. Upon arriving at water station i, Takahashi stops for R_i seconds before resuming running, and Aoki stops for S_i seconds before resuming running (if the time is 0 seconds, they pass through without stopping). However, upon arriving at the goal, water station N, they finish running immediately and do not stop for hydration, regardless of the values of R_N and S_N. A runner who has reached the goal remains at water station N until the end of the observation period.

Both runners start from the start point simultaneously at time 0 and run towards the goal (the direction in which the water station numbers increase) at their respective speeds.

Let f(t) be Takahashi's distance from the start point at time t, and g(t) be Aoki's distance from the start point at time t. We say that one runner overtakes the other when the sign of f(t) - g(t) changes. Strictly speaking, it refers to the occurrence of either of the following:

• There exists a time t_0 such that, for a sufficiently small positive number \varepsilon, f(t) < g(t) holds for t_0 - \varepsilon < t < t_0, and f(t) > g(t) holds for t_0 < t < t_0 + \varepsilon. This corresponds to Takahashi overtaking Aoki.
• There exists a time t_0 such that, for a sufficiently small positive number \varepsilon, f(t) > g(t) holds for t_0 - \varepsilon < t < t_0, and f(t) < g(t) holds for t_0 < t < t_0 + \varepsilon. This corresponds to Aoki overtaking Takahashi.

If f(t) = g(t) persists for some duration before their relative order changes, this is also counted as 1 overtaking. On the other hand, if f(t) = g(t) occurs but their relative order does not change afterwards, it is not counted as an overtaking.

Please note the following:

• At time 0, both runners are at the same position (the start point). Since there is no relative order before departure, one runner pulling ahead immediately after starting is not counted as an overtaking.
• The end of the observation period is the time T when the slower of the two runners arrives at water station N. If their relative order changes exactly at time T (i.e., t_0 = T in the definition above), it is not counted as an overtaking because the state after t_0 cannot be observed.
• If one runner passes the other who is stopped at a water station, changing their relative order, this is also counted as an overtaking according to the definition above.

Find the total number of overtakings that occur from the time they start at time 0 until time T. Count both the cases where Takahashi overtakes Aoki and where Aoki overtakes Takahashi.

Constraints

• 1 \leq N \leq 5 \times 10^5
• 1 \leq V \leq 10^9
• 1 \leq W \leq 10^9
• V \neq W
• 0 \leq R_i \leq 10^9 (1 \leq i \leq N)
• 0 \leq S_i \leq 10^9 (1 \leq i \leq N)
• All input values are integers.

Sample Input 1

3 2 1
0 3 0
1 0 0

Sample Output 1

1

Sample Input 2

4 1 3
2 0 4 0
0 5 0 0

Sample Output 2

2

Sample Input 3

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

Sample Output 3

5

Sample Input 4

30 7 11
0 8 0 3 12 1 0 6 4 0 10 2 5 0 7 1 0 9 3 0 11 2 6 0 4 8 0 5 1 0
4 0 9 1 0 7 2 5 0 11 3 0 6 2 0 8 1 4 0 10 2 0 7 3 0 9 1 6 0 0

Sample Output 4

8

Sample Input 5

1 1000000000 1
1000000000
0

Sample Output 5

0