Siruseri happens to have some of the best chess player in Indian and one of the most important events in the Siruseri sports calendar is the Annual Chees Challenge where teams from Siruseri and Navalur compete. The event is held alternately at Siruseri and Navalur. This year the tournament is to be held at Siruseri. Since starting a war or accusing Navalur of possessing a weapon of mass destruction is beyond his scope (and he also has a few more brain cells than the average leader of the free world) he decided to do something clever. Draw Fixing!!
To understand what he intended to do, we need to know how the Chees Challenge match is organized. Both Siruseri and Navalur are required to send N players. Every player from both teams participates in exactly one game (and so exactly N games are played). The host is expected to draw lots to determine who plays who. Our secretary plans to fix this draw so that the pairing are exactly as he wants them to be. Each chees player has an ELO rating indicating how good he is. The higher the rating the better the player. The secretary knows the rating of each of the player in the Siruseri and Navalur team and he would like to pair theme up so that the number of pair in which the Siruseri player and Navalur has a higher ELO rating is maximized.For example, supposed that N is 4 and the rating of the player are as below.
Siruseri Team ELO Rating Navalur Team ELO Rating
Player 1 8173 Player 1 2450
Player 2 2134 Player 2 1860
Player 3 1900 Player 3 1700
Player 4 1600 Player 4 2120
Then the secretary can arrange for Siruseri to have higher rating in 3 out of 4 games. He can do this, for example, by pairing them as (1,2), (2,4), (3,3) and (4,1), where (i,j) means Player i from Siruseri plays Player j from Navalur. This is the best he can do as no player from Siruseri can beat Player 1 from Navalur.Your task is help the secretary to find a pairing that maximizes the number of pairs with higher rating for Siruseri.
The first line of the input contains a single integer N, denoting the number of player in each team. The next N lines (Lines 2 through N+1) list the ratings of the N players in the Siruseri team and the N following lines (Lines+2 through 2N+1) denote the rating of the players in the Navalur team.
The first line of the output is an integer N (0 ≤ N ≤N) representing the number of pairs where the Siruseri player has a higher rating in the optimal pairing. This should be followed by N lines, each containing a pair indicating the player chosen from the Siruseri team to play against from the player from Navalur.
We illustrate the input and output format using the example above.
1 vs. 2
2 vs. 4
3 vs. 3 and
4 vs. 1