There are $L\times(L+1)\times(L+2)/6$ stones. Snuke stacked these stones like a tetrahedron (a 3D object that consists of four triangular faces). The position of a stone is represented by a tuple of integers $(i,j,k)$ ($1\le k\le j\le i\le L$). When $i<L$, the stone at $(i,j,k)$ is stacked on top of three stones at $(i+1,j,k)$, $(i+1,j+1,k)$, and $(i+1,j+1,k+1)$.

Snuke colors these stones in the following way. First, he colors all stones in the bottommost layer. For each $i$ ($1\le i\le N$), he colors the stone at $(L,A_i,B_i)$ black, and colors the other stones on the bottommost layer white. Then, he colors the other stones from bottom to top. He colors the stone at $(i,j,k)$ black if the number of black stones below it ($(i+1,j,k)$, $(i+1,j+1,k)$, and $(i+1,j+1,k+1)$) is either zero or two. Otherwise he paints this stone white.

Determine the color of the topmost stone.

Input

$$ L\ N\\ A_1\ B_1\\ \vdots\\ A_N\ B_N $$

• $2\le L\le 10^9$
• $0\le N\le\min(1000,L\times(L+1)/2)$
• $1\le B_i\le A_i\le L$
• The tuples $(A_i,B_i)$ are pairwise distinct.

Output

Print “Tori” if the topmost stone is black. Otherwise print “Yayoi”.

Examples

Input 1

2 2
2 1
1 1

Output 1

Tori

Input 2

3 0

Output 2

Yayoi