Given a sequence $A_1, A_2, \ldots, A_N$ of length $N$. Write a program that processes the following queries:

• 1 x v: Change $A_x$ to $v$.

• 2 k b_1 ... b_k: If the sequence $A$ can be partitioned into intervals satisfying the following conditions, output "TAK", otherwise output "NIE".

  • Each number belongs to exactly one interval.
  • Intervals must not overlap.
  • The XOR of all numbers in each interval must be equal to one of $b_1, \ldots, b_k$.

Input

The first line contains the length $N$ of the sequence. ($1 \le N \le 100{,}000$)

The second line contains $A_1, A_2, \ldots, A_N$. ($0 \le A_i < 2^{20}$)

The third line contains the number of queries $M$. ($1 \le M$)

The next $M$ lines each describe a query. ($1 \le x \le N$, $0 \le v, b_i < 2^{20}$, $1 \le k \le 5$)

The number of type 1 queries does not exceed $400{,}000$, and the total sum of $k$ over all type 2 queries does not exceed $100{,}000$.

Output

Output the results of type 2 queries.

Examples

Input 1

5
1 2 0 3 0
10
2 1 3
2 1 0
1 3 5
2 2 6 3
1 1 8
1 2 5
1 3 3
1 4 1
1 5 1
2 3 2 4 8

Output 1

TAK
TAK
TAK
NIE