Dr.Kong has entered a bobsled competition because he hopes his hefty weight will give his an

advantage

 over the L meter course (2 <= L<= 1000).

Dr.Kong will push off the starting line at 1 meter per second, but  his speed can change while he

rides

 along the course. Near the middle of every meter Bessie travels, he can change his  speed 

either by

 using gravity to accelerate by one meter per second or by braking to stay at the same speed or

decrease

 his speed by one meter per second.

Naturally, Dr.Kong must negotiate N (1 <= N <= 500) turns on the way down the hill. Turn i is

located

 T_i  meters from the course start (1 <= T_i <= L-1), and  he must be enter the corner meter at 

a peed of at most S_i  meters per second (1 <= S_i <= 1000).

  Dr.Kong can cross the finish line at any speed he likes.

Help Dr.Kong learn the fastest speed he can attain without exceeding the speed limits on the

turns.

Consider this course with the meter markers as integers and the  turn speed limits in brackets

(e.g., '[3]'):

0    1   2   3   4   5   6   7[3]   8   9  10  11[1]  12   13[8]    14                   

(Start) |------------------------------------------------------------------------------------- ---------à| 

(Finish)  

Below is a chart of  Dr.Kong 's speeds at the beginning of each meter length of the course:

Max:                               [3]             [1]      [8]

Mtrs:   0   1   2   3   4   5   6   7   8   9  10  11  12   13   14

Spd:    1   2   3   4   5   5   4   3   4   3   2   1   2   3    4

His maximum speed was 5 near the beginning of meter 4.

Line 1:       Two space-separated integers: L and N

Lines 2..N+1:  Line i+1 describes turn i with two space-separated  integers: T_i and S_i

 Line 1:   A single integer Line 1:   A single integer,  representing the maximum speed which  Dr.Kong can attain between

the start and the finish line,  inclusi