Two thousand years ago, someone took the first step towards defeating the Dark Lord. Now, Yuria and friends are continuing that journey. However, before they can defeat the Dark Lord, they must first defeat their crippling boredom, since as it turns out, riding on a wagon for months on end is not the most fun experience. Thus, Yuria has devised a game that she and her party can play while on the road. Yuria creates an array of $$$N$$$ ($$$1 \le N \le 2 \cdot 10^5$$$) $$$1$$$'s and $$$0$$$'s, represented by the array $$$a_1, a_2, \ldots, a_N$$$ ($$$0 \le a_i \le 1$$$). Then, she will perform $$$Q$$$ ($$$1 \le Q \le 2 \cdot 10^5$$$) queries on the array:

• "1 l r" — Flip the values of all values in the subarray $$$a_l, a_{l + 1}, \ldots, a_r$$$. Formally, set $$$a_i = (a_i + 1)\%2$$$ for all $$$l \le i \le r$$$.
• "2 l r" — Play a game using the values in the subarray $$$a_l, a_{l + 1}, \ldots, a_r$$$, where players take turns selecting a maximal subarray containing either all $$$1$$$'s or all $$$0$$$'s and remove it. The player who cannot make a move loses. Note that any subarray a player chooses must be maximal, meaning that it cannot be contained by a larger subarray containing all $$$1$$$'s or all $$$0$$$'s. Since Yuria is not very responsible at cleaning up after herself, after playing the game, all of the values in the subarray will be reset to $$$0$$$, ie. $$$a_i = 0$$$ for all $$$l \le i \le r$$$. Please tell Yuria if she will win as the player who makes the first move.