Once in a casino

## 题目大意 给定两个长度都为n$(1\leq n\leq 10^5)$的数字串A和B，你可以执行若干次操作，每次操作是将相邻的两个位置+1或-1，要求不能对数字串以外的位置进行操作，且操作中每个数字都必须在$[0,9]$中。求把A变成B所执行的最小操作数c，并输出前$\min(c,10^5)$个操作，无解输出-1。 ## 输入格式 第一行一个正整数n表示A和B的长度。 接下来有两行，每行一个长度为n的数字串表示A和B。 ## 输出格式 如果不可能把A变成B，输出-1。 否则第一行输出最小操作数c。 接下来输出$num=\min(c,10^5)$行，表示前num个操作，第 i 行输出两个整数$d_i,s_i(1\leq l\leq n-1,s=\pm 1)$，表示第 i 个操作将$a_{d_i}$和$a_{d_i+1}$加上$s_i$。

One player came to a casino and found a slot machine where everything depends only on how he plays. The rules follow. A positive integer $ a $ is initially on the screen. The player can put a coin into the machine and then add $ 1 $ to or subtract $ 1 $ from any two adjacent digits. All digits must remain from $ 0 $ to $ 9 $ after this operation, and the leading digit must not equal zero. In other words, it is forbidden to add $ 1 $ to $ 9 $ , to subtract $ 1 $ from $ 0 $ and to subtract $ 1 $ from the leading $ 1 $ . Once the number on the screen becomes equal to $ b $ , the player wins the jackpot. $ a $ and $ b $ have the same number of digits. Help the player to determine the minimal number of coins he needs to spend in order to win the jackpot and tell how to play.

The first line contains a single integer $ n $ ( $ 2 \le n \le 10^5 $ ) standing for the length of numbers $ a $ and $ b $ . The next two lines contain numbers $ a $ and $ b $ , each one on a separate line ( $ 10^{n-1} \le a, b < 10^n $ ).

If it is impossible to win the jackpot, print a single integer $ -1 $ . Otherwise, the first line must contain the minimal possible number $ c $ of coins the player has to spend. $ \min(c, 10^5) $ lines should follow, $ i $ -th of them containing two integers $ d_i $ and $ s_i $ ( $ 1\le d_i\le n - 1 $ , $ s_i = \pm 1 $ ) denoting that on the $ i $ -th step the player should add $ s_i $ to the $ d_i $ -th and $ (d_i + 1) $ -st digits from the left (e. g. $ d_i = 1 $ means that two leading digits change while $ d_i = n - 1 $ means that there are two trailing digits which change). Please notice that the answer may be very big and in case $ c > 10^5 $ you should print only the first $ 10^5 $ moves. Your answer is considered correct if it is possible to finish your printed moves to win the jackpot in the minimal possible number of coins. In particular, if there are multiple ways to do this, you can output any of them.

3
223
322

2
1 1
2 -1

2
20
42

2
1 1
1 1

2
35
44

-1

In the first example, we can make a +1 operation on the two first digits, transforming number $ \textbf{22}3 $ into $ \textbf{33}3 $ , and then make a -1 operation on the last two digits, transforming $ 3\textbf{33} $ into $ 3\textbf{22} $ . It's also possible to do these operations in reverse order, which makes another correct answer. In the last example, one can show that it's impossible to transform $ 35 $ into $ 44 $ .