401365: GYM100418 E Hamilton traversal 2

You have a K-dimentional parallelepiped with dimensions N₁, N₂... N_k You should traversal the parallelepiped in order to visit each cell only at once and returning into the original one. In one operation you can move into the neighboring cell either by coordinate N₁ N₂ ... or N_k.

The first line of the input contains one integer K — number of dimensions. The second line contains K integer numbers N₁, N₂... N_k The third line contains K integers X₁, X₂... X_k representing your initial position.

Constraints: The product of N₁, N₂... N_k will be between 1 and 10⁶ inclusive. K will be between 2 and 10.

The output should contain the word No if there is no such traversal. In the other case output the word Yes. The following lines should contain a string in the format “C <+,->” where C is the coordinate, + or - denote the increase or decrease of this coordinate respectively. Please see the samples below for the details.

3
2 2 2
1 2 2

Yes
2 -
3 -
2 +
1 +
2 -
3 +
2 +
1 -