Jetpack Joyride is a 2011 side-scrolling endless runner action video game. The game uses a simple, one-touch system to control the jetpack; when the player presses anywhere on the touchscreen, the jetpack fires and Barry rises. When the player lets go, the jetpack turns off, and Barry falls. Because he is continually in motion, the player does not control his speed, simply his movement along the vertical axis.(Wikipedia)

Cuber QQ is playing on a modified version of this game. The map can be regarded as an infinite 2d-plane. We assume that the player's position is at the -th frame(). For any valid sequence , since the player starts at . Also, there must exist a sequence , such that:



There are coins on the map, the -th coin is at . By coincidence, is strictly increasing, and the -th coin has value . The player can get a coin, if and only if . Cuber QQ wants to know: the largest possible total value of coins he can get by playing only once. Output this number in its binary representation.

The first line contains an integer , denoting the number of test cases.

In each test case, the first line contains an integer (). In the next  lines, the -th line contains two integers  and .

It is guaranteed that , , and . Note that you should use efficient input method.

 lines, each line contains an 01-string of length , denoting the binary representation of the answer. If the answer has less than  bits, you should add zeros in the front.

3
5
1 -2
3 0
4 2
8 2
9 0
3
2 3
4 3
5 2
9
68 796
75 1062
79 1219
173 1490
286 -9172
420 -22332
498 -30897
831 -106035
956 -122043

01111
100
111111111

We use red crosses to represent coins and black dots to represent the player's flying route. Here is the explanation for the first test case: