13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T6f9,

Dabir, Egor, and Arseniy just got on the train and decided to play a game. Dabir has a backpack with an infinite number of cubes. He built $$$n$$$ towers from them, where the $$$i$$$-th tower has height $$$h_i$$$ cubes.

Egor and Arseniy must choose an integer $$$x_i$$$ for each tower $$$i$$$ and increase its height by $$$x_i$$$ exactly once. For example, if $$$h$$$ = [$$$1, 3, 2, 2$$$], $$$x$$$ = [$$$3, 2, 2, 8$$$], then after increasing $$$h$$$ it will become [$$$4, 5, 4, 10$$$]. Their goal is to make the heights of all towers equal.

To make the game more interesting, Dabir wants to choose an integer $$$k$$$ and add a restriction: each $$$x_i$$$ must satisfy $$$1 \le x_i \le k$$$. Help him find the smallest $$$k$$$ for which it is possible to finish the game.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

Then $$$t$$$ test cases follow.

The first line of each tes

Games on the Train

Examples